Time-dependent Relativistic Mean-field Theory and Random Phase Approximation
P.Ring; D.Vretenar; A.Wandelt; NguyenVanGiai; MAZhong-yu; CAOLi-gang
2001-01-01
The relativistic random phase approximation (RRPA) is derived from the time-dependent relativistic mean field (TD RMF) theory in the limit of small amplitude oscillations. In the no-sea approximation of the RMF theory, the RRPA configuration space includes not only the usual particle-hole ph-states, but also ah configurations, i.e. pairs formed from occupied states in the Fermi sea and empty negative-energy states in the Dirac sea. The contribution of the negative energy states to the RRPA matrices is examined in a schematic model, and the large effect of Dirac sea states on isoscalar strength distributions is illustrated for the giant monopole resonance in 116Sn. It is shown that
Beyond the relativistic mean-field approximation (III): collective Hamiltonian in five dimensions
Niksic, T; Vretenar, D; Prochniak, L; Meng, J; Ring, P
2008-01-01
The framework of relativistic energy density functionals is extended to include correlations related to restoration of broken symmetries and fluctuations of collective variables. A model is developed for the solution of the eigenvalue problem of a five-dimensional collective Hamiltonian for quadrupole vibrational and rotational degrees of freedom, with parameters determined by constrained self-consistent relativistic mean-field calculations for triaxial shapes. The model is tested in a series of illustrative calculations of potential energy surfaces and the resulting collective excitation spectra and transition probabilities of the chain of even-even gadolinium isotopes.
Relativistic mean field description of cluster radioactivity
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.
Diabatic constrained relativistic mean field approach
L"u, H F; Meng, J
2005-01-01
A diabatic (configuration-fixed) constrained approach to calculate the potential energy surface (PES) of the nucleus is developed in the relativistic mean field model. The potential energy surfaces of $^{208}$Pb obtained from both adiabatic and diabatic constrained approaches are investigated and compared. The diabatic constrained approach enables one to decompose the segmented PES obtained in usual adiabatic approaches into separate parts uniquely characterized by different configurations, to define the single particle orbits at very deformed region by their quantum numbers, and to obtain several well defined deformed excited states which can hardly be expected from the adiabatic PES's.
General Relativistic Mean Field Theory for rotating nuclei
Madokoro, Hideki [Kyushu Univ., Fukuoka (Japan). Dept. of Physics; Matsuzaki, Masayuki
1998-03-01
The {sigma}-{omega} model Lagrangian is generalized to an accelerated frame by using the technique of general relativity which is known as tetrad formalism. We apply this model to the description of rotating nuclei within the mean field approximation, which we call General Relativistic Mean Field Theory (GRMFT) for rotating nuclei. The resulting equations of motion coincide with those of Munich group whose formulation was not based on the general relativistic transformation property of the spinor fields. Some numerical results are shown for the yrast states of the Mg isotopes and the superdeformed rotational bands in the A {approx} 60 mass region. (author)
Relativistic mean-field mass models
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.
Relativistic mean-field mass models
Pena-Arteaga, D.; Goriely, S.; Chamel, N. [Universite Libre de Bruxelles, Institut d' Astronomie et d' Astrophysique, CP-226, Brussels (Belgium)
2016-10-15
We present a new effort to develop viable mass models within the relativistic mean-field approach with density-dependent meson couplings, separable pairing and microscopic estimations for the translational and rotational correction energies. Two interactions, DD-MEB1 and DD-MEB2, are fitted to essentially all experimental masses, and also to charge radii and infinite nuclear matter properties as determined by microscopic models using realistic interactions. While DD-MEB1 includes the σ, ω and ρ meson fields, DD-MEB2 also considers the δ meson. Both mass models describe the 2353 experimental masses with a root mean square deviation of about 1.1 MeV and the 882 measured charge radii with a root mean square deviation of 0.029 fm. In addition, we show that the Pb isotopic shifts and moments of inertia are rather well reproduced, and the equation of state in pure neutron matter as well as symmetric nuclear matter are in relatively good agreement with existing realistic calculations. Both models predict a maximum neutron-star mass of more than 2.6 solar masses, and thus are able to accommodate the heaviest neutron stars observed so far. However, the new Lagrangians, like all previously determined RMF models, present the drawback of being characterized by a low effective mass, which leads to strong shell effects due to the strong coupling between the spin-orbit splitting and the effective mass. Complete mass tables have been generated and a comparison with other mass models is presented. (orig.)
Cluster decay in very heavy nuclei in Relativistic Mean Field
Bhattacharya, Madhubrata
2008-01-01
Exotic cluster decay of very heavy nuclei has been studied in the microscopic Super-Asymmetric Fission Model. Relativistic Mean Field model with the force FSU Gold has been 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 have been used in the double folding model to obtain the potential between the cluster and the daughter. Half life values have been calculated in the WKB approximation and the spectroscopic factors have been extracted. The latter values are seen to have a simple dependence of the mass of the cluster as has been observed earlier. Predictions have been made for some possible decays.
Spurious Shell Closures in the Relativistic Mean Field Model
Geng, L S; Toki, H; Long, W H; Shen, G
2006-01-01
Following a systematic theoretical study of the ground-state properties of over 7000 nuclei from the proton drip line to the neutron drip line in the relativistic mean field model [Prog. Theor. Phys. 113 (2005) 785], which is in fair agreement with existing experimental data, we observe a few spurious shell closures, i.e. proton shell closures at Z=58 and Z=92. These spurious shell closures are found to persist in all the effective forces of the relativistic mean field model, e.g. TMA, NL3, PKDD and DD-ME2.
Quantum Corrections on Relativistic Mean Field Theory for Nuclear Matter
ZHANG Qi-Ren; GAO Chun-Yuan
2011-01-01
We propose a quantization procedure for the nucleon-scalar meson system, in which an arbitrary mean scalar meson field Φ is introduced.The equivalence of this procedure with the usual one is proven for any given value of Φ.By use of this procedure, the scalar meson field in the Walecka's MFA and in Chin's RHA are quantized around the mean field.Its corrections on these theories are considered by perturbation up to the second order.The arbitrariness of Φ makes us free to fix it at any stage in the calculation.When we fix it in the way of Walecka's MFA, the quantum corrections are big, and the result does not converge.When we fix it in the way of Chin's RHA, the quantum correction is negligibly small, and the convergence is excellent.It shows that RHA covers the leading part of quantum field theory for nuclear systems and is an excellent zeroth order approximation for further quantum corrections, while the Walecka's MFA does not.We suggest to fix the parameter Φ at the end of the whole calculation by minimizing the total energy per-nucleon for the nuclear matter or the total energy for the finite nucleus, to make the quantized relativistic mean field theory (QRMFT) a variational method.
Cranked Relativistic Mean Field Description of Superdeformed Rotational Bands
Afanasjev, A. V.; Lalazissis, G. A.; Ring, P.
1997-01-01
The cranked relativistic mean field theory is applied for a detailed investigation of eight superdeformed rotational bands observed in $^{151}$Tb. It is shown that this theory is able to reproduce reasonably well not only the dynamic moments of inertia $J^{(2)}$ of the observed bands but also the alignment properties of the single-particle orbitals.
Cluster decay in very heavy nuclei in Relativistic Mean Field
Bhattacharya, Madhubrata; Gangopadhyay, G.
2008-01-01
Exotic cluster decay of very heavy nuclei has been studied in the microscopic Super-Asymmetric Fission Model. Relativistic Mean Field model with the force FSU Gold has been 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 have been used in the double folding model to obtain the potential between the cluster and the daughter. Half life values have been ca...
Modified Mean Field approximation for the Ising Model
Di Bartolo, Cayetano
2009-01-01
We study a modified mean-field approximation for the Ising Model in arbitrary dimension. Instead of taking a "central" spin, or a small "drop" of fluctuating spins coupled to the effective field of their nearest neighbors as in the Mean-Field or the Bethe-Peierls-Weiss methods, we take an infinite chain of fluctuating spins coupled to the mean field of the rest of the lattice. This results in a significative improvement of the Mean-Field approximation with a small extra effort.
Relativistic Mean Field Study on Halo Structures of Mirror Nuclei
LIANG Yu-Jie; LI Yan-Song; LIU Zu-Hua; ZHOU Hong-Yu
2009-01-01
Halo structures of some light mirror nuclei are investigated with the relativistic mean field (RMF) theory.The calculations show that the dispersion of the valence proton is larger than that of the valence neutron in its mirror nucleus,the difference between the root-mean-square (rms) radius of the valence nucleon in each pair of mirror nuclei becomes smailer with the increase of the mass number A,and all the ratios of the rms radius of the valence nucleon to that of the matter in each pair o~ mirror nuclei decrease almost linearly with the increase of the mass number A.
A New Parameter Set for the Relativistic Mean Field Theory
Nerlo-Pomorska, B; Nerlo-Pomorska, Bozena; Sykut, Joanna
2004-01-01
Subtracting the Strutinsky shell corrections from the selfconsistent energies obtained within the Relativistic Mean Field Theory (RMFT) we have got estimates for the macroscopic part of the binding energies of 142 spherical even-even nuclei. By minimizing their root mean square deviations from the values obtained with the Lublin-Srasbourg Drop (LSD) model with respect to the nine RMFT parameters we have found the optimal set (NL4). The new parameters reproduce also the radii of these nuclei with an accuracy comparable with that obtained with the NL1 and NL3 sets.
Relativistic Consistent Angular-Momentum Projected Shell-Model:Relativistic Mean Field
LI Yan-Song; LONG Gui-Lu
2004-01-01
We develop a relativistic nuclear structure model, relativistic consistent angular-momentum projected shellmodel (RECAPS), which combines the relativistic mean-field theory with the angular-momentum projection method.In this new model, nuclear ground-state properties are first calculated consistently using relativistic mean-field (RMF)theory. Then angular momentum projection method is used to project out states with good angular momentum from a few important configurations. By diagonalizing the hamiltonian, the energy levels and wave functions are obtained.This model is a new attempt for the understanding of nuclear structure of normal nuclei and for the prediction of nuclear properties of nuclei far from stability. In this paper, we will describe the treatment of the relativistic mean field. A computer code, RECAPS-RMF, is developed. It solves the relativistic mean field with axial-symmetric deformation in the spherical harmonic oscillator basis. Comparisons between our calculations and existing relativistic mean-field calculations are made to test the model. These include the ground-state properties of spherical nuclei 16O and 208Pb,the deformed nucleus 20Ne. Good agreement is obtained.
COMPRESSIBILITY OF NUCLEI IN RELATIVISTIC MEAN FIELD-THEORY
BOERSMA, HF; MALFLIET, R; SCHOLTEN, O
1991-01-01
Using the relativistic Hartree approximation in the sigma-omega model we study the isoscalar giant monopole resonance. It is shown that the ISGMR of lighter nuclei has non-negligible anharmonic terms. The compressibility of nuclear matter is determined using a leptodermous expansion.
Merging Belief Propagation and the Mean Field Approximation
Riegler, Erwin; Kirkelund, Gunvor Elisabeth; Manchón, Carles Navarro
2010-01-01
We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al., which allows to use the same objective function (Kullback-Leibler divergence...
Relativistic Mean-Field Models and Nuclear Matter Constraints
Dutra, M; Carlson, B V; Delfino, A; Menezes, D P; Avancini, S S; Stone, J R; Providência, C; Typel, S
2013-01-01
This work presents a preliminary study of 147 relativistic mean-field (RMF) hadronic models used in the literature, regarding their behavior in the nuclear matter regime. We analyze here different kinds of such models, namely: (i) linear models, (ii) nonlinear \\sigma^3+\\sigma^4 models, (iii) \\sigma^3+\\sigma^4+\\omega^4 models, (iv) models containing mixing terms in the fields \\sigma and \\omega, (v) density dependent models, and (vi) point-coupling ones. In the finite range models, the attractive (repulsive) interaction is described in the Lagrangian density by the \\sigma (\\omega) field. The isospin dependence of the interaction is modeled by the \\rho meson field. We submit these sets of RMF models to eleven macroscopic (experimental and empirical) constraints, used in a recent study in which 240 Skyrme parametrizations were analyzed. Such constraints cover a wide range of properties related to symmetric nuclear matter (SNM), pure neutron matter (PNM), and both SNM and PNM.
Back-reaction beyond the mean field approximation
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.
A new approach to spinel ferrites through mean field approximation
Yazdani, A. [Tarbyat Modares University, Tehran P.C 14115-175 (Iran, Islamic Republic of)]. E-mail: yazdania@modares.ac.ir; Jalilian Nosrati, M.R. [Islamic Azad University Central Tehran Branch, Tehran P.C 14168-94351 (Iran, Islamic Republic of); Ghasemi, R. [Islamic Azad University Central Tehran Branch, Tehran P.C 14168-94351 (Iran, Islamic Republic of)
2006-09-15
The magnetic behavior and specification of spinel ferrites regarding exchange interactions is being studied. The strength of interactions has been examined through the cation substitution with application of mean field approximation of exchange interaction J{sub ij} . Two correlation and approximation parameters have been defined: correlation length R {sub c} in super-exchange and the magnetic effect of ion on the electron fluctuation J {sub 0}.
Relativistic mean-field models and nuclear matter constraints
Dutra, M.; Lourenco, O.; Carlson, B. V. [Departamento de Fisica, Instituto Tecnologico de Aeronautica-CTA, 12228-900, Sao Jose dos Campos, SP (Brazil); Delfino, A. [Instituto de Fisica, Universidade Federal Fluminense, 24210-150, Boa Viagem, Niteroi, RJ (Brazil); Menezes, D. P.; Avancini, S. S. [Departamento de Fisica, CFM, Universidade Federal de Santa Catarina, CP. 476, CEP 88.040-900, Florianopolis, SC (Brazil); Stone, J. R. [Oxford Physics, University of Oxford, OX1 3PU Oxford (United Kingdom) and Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996 (United States); Providencia, C. [Centro de Fisica Computacional, Department of Physics, University of Coimbra, P-3004-516 Coimbra (Portugal); Typel, S. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Theorie, Planckstrasse 1,D-64291 Darmstadt (Germany)
2013-05-06
This work presents a preliminary study of 147 relativistic mean-field (RMF) hadronic models used in the literature, regarding their behavior in the nuclear matter regime. We analyze here different kinds of such models, namely: (i) linear models, (ii) nonlinear {sigma}{sup 3}+{sigma}{sup 4} models, (iii) {sigma}{sup 3}+{sigma}{sup 4}+{omega}{sup 4} models, (iv) models containing mixing terms in the fields {sigma} and {omega}, (v) density dependent models, and (vi) point-coupling ones. In the finite range models, the attractive (repulsive) interaction is described in the Lagrangian density by the {sigma} ({omega}) field. The isospin dependence of the interaction is modeled by the {rho} meson field. We submit these sets of RMF models to eleven macroscopic (experimental and empirical) constraints, used in a recent study in which 240 Skyrme parametrizations were analyzed. Such constraints cover a wide range of properties related to symmetric nuclear matter (SNM), pure neutron matter (PNM), and both SNM and PNM.
Green's function relativistic mean field theory for Λ hypernuclei
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.
Hot and dense matter beyond relativistic mean field theory
Zhang, Xilin
2016-01-01
Properties of hot and dense matter are calculated in the framework of quantum hadro-dynamics by including contributions from two-loop (TL) diagrams arising from the exchange of iso-scalar and iso-vector mesons between nucleons. Our extension of mean-field theory (MFT) employs the same five density-independent coupling strengths which are calibrated using the empirical properties at the equilibrium density of iso-spin symmetric matter. Results of calculations from the MFT and TL approximations are compared for conditions of density, temperature, and proton fraction encountered in astrophysics applications involving compact objects. The TL results for the equation of state (EOS) of cold pure neutron matter at sub- and near-nuclear densities agree well with those of modern quantum Monte Carlo and effective field-theoretical approaches. Although the high-density EOS in the TL approximation for neutron-star matter is substantially softer than its MFT counterpart, it is able to support a $2M_\\odot$ neutron star req...
Benchmarking mean-field approximations to level densities
Alhassid, Y; Gilbreth, C N; Nakada, H
2015-01-01
We assess the accuracy of finite-temperature mean-field theory using as a standard the Hamiltonian and model space of the shell model Monte Carlo calculations. Two examples are considered: the nucleus $^{162}$Dy, representing a heavy deformed nucleus, and $^{148}$Sm, representing a nearby heavy spherical nucleus with strong pairing correlations. The errors inherent in the finite-temperature Hartree-Fock and Hartree-Fock-Bogoliubov approximations are analyzed by comparing the entropies of the grand canonical and canonical ensembles, as well as the level density at the neutron resonance threshold, with shell model Monte Carlo (SMMC) calculations, which are accurate up to well-controlled statistical errors. The main weak points in the mean-field treatments are seen to be: (i) the extraction of number-projected densities from the grand canonical ensembles, and (ii) the symmetry breaking by deformation or by the pairing condensate. In the absence of a pairing condensate, we confirm that the usual saddle-point appr...
Relativistic heavy ion collisions with realistic non-equilibrium mean fields
Fuchs, C; Wolter, H H
1996-01-01
We study the influence of non-equilibrium phase space effects on the dynamics of heavy ion reactions within the relativistic BUU approach. We use realistic Dirac-Brueckner-Hartree-Fock (DBHF) mean fields determined for two-Fermi-ellipsoid configurations, i.e. for colliding nuclear matter, in a local phase space configuration approximation (LCA). We compare to DBHF mean fields in the local density approximation (LDA) and to the non-linear Walecka model. The results are further compared to flow data of the reaction Au on Au at 400 MeV per nucleon measured by the FOPI collaboration. We find that the DBHF fields reproduce the experiment if the configuration dependence is taken into account. This has also implications on the determination of the equation of state from heavy ion collisions.
Description of Drip-Line Nuclei within Relativistic Mean-Field Plus BCS Approach
Yadav, H L; Toki, H
2004-01-01
Recently it has been demonstrated, considering Ni and Ca isotopes as prototypes, that the relativistic mean-field plus BCS (RMF+BCS) approach wherein the single particle continuum corresponding to the RMF is replaced by a set of discrete positive energy states for the calculation of pairing energy provides a good approximation to the full relativistic Hartree-Bogoliubov (RHB) description of the ground state properties of the drip-line neutron rich nuclei. The applicability of RMF+BCS is essentially due to the fact that the main contribution to the pairing correlations is provided by the low-lying resonant states. General validity of this approach is demonstrated by the detailed calculations for the ground state properties of the chains of isotopes of O, Ca, Ni, Zr, Sn and Pb nuclei. The TMA and NL-SH force parameter sets have been used for the effective mean-field Lagrangian. Comprehensive results for the two neutron separation energy, rms radii, single particle pairing gaps and pairing energies etc. are pres...
Ground State Properties of Ds Isotopes Within the Relativistic Mean Field Theory
张海飞; 张鸿飞; 李君清
2012-01-01
The ground state properties of Ds (Z=110) isotopes (N=151-195) are studied in the framework of the relativistic mean field (RMF) theory with the effective interaction NL-Z2.The pairing correlation is treated within the conventional BCS approximation.The calculated binding energies are consistent with the results from finite-range droplet model (FRDM) and Macroscopic-microscopic method (MMM).The quadrupole deformation,α-decay energy,α-decay half-live,charge radius,two-neutron separation energy and single-particle spectra are analyzed for Ds isotopes to find new characteristics of superheavy nuclei (SHN).Among the calculated results it is rather distinct that the isotopic shift appears evidently at neutron number N=184.
Cluster decay in very heavy nuclei in a relativistic mean field model
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.
Multiple chiral doublet candidate nucleus $^{105}$Rh in a relativistic mean-field approach
Li, Jian; Meng, J; 10.1103/PhysRevC.83.037301
2011-01-01
Following the reports of two pairs of chiral doublet bands observed in $^{105}$Rh, the adiabatic and configuration-fixed constrained triaxial relativistic mean-field (RMF) calculations are performed to investigate their triaxial deformations with the corresponding configuration and the possible multiple chiral doublet (M$\\chi$D) phenomenon. The existence of M$\\chi$D phenomenon in $^{105}$Rh is highly expected.
Shape Coexistence for 179Hg in Relativistic Mean-Field Theory
WANG Nan; MENG Jie; ZHAO En-Guang
2005-01-01
The potential energy surface of179 Hg is traced and the multi-shape coexistence phenomenon in that nucleus is studied within the relativistic mean-field theory with quadrupole moment constraint. The calculation results of binding energies and charge radii of mercury isotopes are in good agreement with the experimental data.
One-Proton Halo in 31Cl with Relativistic Mean-Field Theory
蔡翔舟; 沈文庆; 任中洲; 蒋维洲; 方德清; 张虎勇; 钟晨; 魏义彬; 郭威; 马余刚; 朱志远
2002-01-01
We investigate proton-rich isotopes s1,32Cl using the nonlinear relativistic mean-field model. It is shown that this model can reproduce the properties of these nuclei well. A long tail appears in the calculated proton density distribution of 31 Cl. The results of relativistic density-dependent Hartree theory show a similar trend of tail density distribution. It is strongly suggested that there is a proton halo in 31Cl and it is indicated that there may be a proton skin in 32 Cl. The relation between the proton halo in 31Cl and the new proton magic number is discussed.
Properties and structure of N=Z nuclei within relativistic mean field theory
GAO Yuan; DONG Jian-Min; ZHANG Hong-Fei; ZUO Wei; LI Jun-Qing
2009-01-01
The axially deformed relativistic mean field theory with the force NLSH has been performed in the blocked BCS approximation to investigate the properties and structure of N=Z nuclei from Z=20 to Z=48.Some ground state quantities such as binding energies, quadrupole deformations, one/two-nucleon separation energies, root-mean-square (rms) radii of charge and neutron, and shell gaps have been calculated.The results suggest that large deformations can be found in medium-heavy nuclei with N=Z=38-42.The charge and neutron rms radii increase rapidly beyond the magic number N=Z=28 until Z=42 with increasing nucleon number, which is similar to isotope shift, yet beyond Z=42, they decrease dramatically as the structure changes greatly from Z=42 to Z=43.The evolution of shell gaps with proton number Z can be clearly observed.Besides the appearance of possible new shell closures, some conventional shell closures have been found to disappear in some region.In addition, we found that the Coulomb interaction is not strong enough to breakdown the shell structure of protons in the current region.
Nuclear matter fourth-order symmetry energy in relativistic mean field models
Cai, Bao-Jun
2011-01-01
Within the nonlinear relativistic mean field model, we derive the analytical expression of the nuclear matter fourth-order symmetry energy $E_{4}(\\rho)$. Our results show that the value of $E_{4}(\\rho)$ at normal nuclear matter density $\\rho_{0}$ is generally less than 1 MeV, confirming the empirical parabolic approximation to the equation of state for asymmetric nuclear matter at $\\rho_{0}$. On the other hand, we find that the $E_{4}(\\rho)$ may become nonnegligible at high densities. Furthermore, the analytical form of the $E_{4}(\\rho)$ provides the possibility to study the higher-order effects on the isobaric incompressibility of asymmetric nuclear matter, i.e., $K_{\\mathrm{sat}}(\\delta)=K_{0}+K_{\\mathrm{{sat},2}}\\delta ^{2}+K_{\\mathrm{{sat},4}}\\delta ^{4}+\\mathcal{O}(\\delta ^{6})$ where $\\delta =(\\rho_{n}-\\rho_{p})/\\rho $ is the isospin asymmetry, and we find that the value of $K_{\\mathrm{{sat},4}}$ is generally comparable with that of the $K_{\\mathrm{{sat},2}}$. In addition, we study the effects of the $E...
The Accuracy of Mean-Field Approximation for Susceptible-Infected-Susceptible Epidemic Spreading
Qu, Bo
2016-01-01
The epidemic spreading has been studied for years by applying the mean-field approach in both homogeneous case, where each node may get infected by an infected neighbor with the same rate, and heterogeneous case, where the infection rates between different pairs of nodes are different. Researchers have discussed whether the mean-field approaches could accurately describe the epidemic spreading for the homogeneous cases but not for the heterogeneous cases. In this paper, we explore under what conditions the mean-field approach could perform well when the infection rates are heterogeneous. In particular, we employ the Susceptible-Infected-Susceptible (SIS) model and compare the average fraction of infected nodes in the metastable state obtained by the continuous-time simulation and the mean-field approximation. We concentrate on an individual-based mean-field approximation called the N-intertwined Mean Field Approximation (NIMFA), which is an advanced approach considered the underlying network topology. Moreove...
Systematic nuclear structure studies using relativistic mean field theory in mass region A ˜ 130
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).
Proton rich nuclei at and beyond the proton drip line in the Relativistic Mean Field theory
Geng, L S; Meng, J
2003-01-01
The Relativistic Mean Field theory is applied to the analysis of ground-state properties of deformed proton-rich odd-Z nuclei in the region $55\\le Z \\le 73$ >. The model uses the TMA and NL3 effective interactions in the mean-field Lagrangian, and describes pairing correlations by the density-independent delta-function interaction. The model predicts the location of the proton drip line, the ground-state quadrupole deformation, one-proton separation energy at and beyond the proton drip line, the deformed single-particle orbital occupied by the odd valence proton and the corresponding spectroscopic factor. The results are in good agreement with the available experimental data except for some odd-odd nuclei in which the proton-neutron pairing may become important and are close to those of Relativistic Hartree-Bogoliubov model.
Description of $^{178}$Hf$^{m2}$ in the constrained relativistic mean field theory
Wei, Zhang; Shuang-Quan, Zhang
2009-01-01
The properties of the ground state of $^{178}$Hf and the isomeric state $^{178}$Hf$^{m2}$ are studied within the adiabatic and diabatic constrained relativistic mean field (RMF) approaches. The RMF calculations reproduce well the binding energy and the deformation for the ground state of $^{178}$Hf. Using the ground state single-particle eigenvalues obtained in the present calculation, the lowest excitation configuration with $K^\\pi=16^+$ is found to be $\
Restoration of rotational symmetry in deformed relativistic mean-field theory
YAO Jiang-Ming; MENG Jie; Pena Arteaga Daniel; Ring Peter
2009-01-01
We report on a very recently developed three-dimensional angular momentum projected relativistic mean-field theory with point-coupling interaction (3DAMP+RMF-PC). Using this approach the same effective nucleon-nucleon interaction is adopted to describe both the single-particle and collective motions in nuclei.Collective states with good quantum angular momentum are built projecting out the intrinsic deformed meanfield states. Results for 24Mg are shown as an illustrative application.
Finite Size Corrected Relativistic Mean-Field Model and QCD Critical End Point
Uddin, Saeed; Ahmad, Jan Shabir
2012-01-01
The effect of finite size of hadrons on the QCD phase diagram is analyzed using relativistic mean field model for the hadronic phase and the Bag model for the QGP phase. The corrections to the EOS for hadronic phase are incorporated in a thermodynamic consistent manner for Van der Waals like interaction. It is found that the effect of finite size of baryons is to shift CEP to higher chemical potential values.
Relativistic mean field study of the superdeformed rotational bands in the A {approx} 60 mass region
Madokoro, Hideki [Dept. of Physics, Kyushu Univ., Fukuoka (Japan); Matsuzaki, Masayuki
1999-03-01
The superdeformed rotational bands in {sup 62}Zn, which were recently discovered, are examined using Relativistic Mean Field model. The experimental dynamical moments of inertia and deformations are well reproduced, but the calculated bands which seem to correspond to the experimental data do not become yrast. This seems to be connected with the wrong position of the g{sup 9/2} single neutron orbit. (author)
Antimagnetic rotation in 108,110In with tilted axis cranking relativistic mean-field approach
Sun, Wu-Ji; Xu, Hai-Dan; Li, Jian; Liu, Yong-Hao; Ma, Ke-Yan; Yang, Dong; Lu, Jing-Bing; Ma, Ying-Jun
2016-08-01
Based on tilted axis cranking relativistic mean-field theory within point-coupling interaction PC-PK1, the rotational structure and the characteristic features of antimagnetic rotation for ΔI = 2 bands in 108,110In are studied. Tilted axis cranking relativistic mean-field calculations reproduce the experimental energy spectrum well and are in agreement with the experimental I ∼ ω plot, although the calculated spin overestimates the experimental values. In addition, the two-shears-like mechanism in candidate antimagnetic rotation bands is clearly illustrated and the contributions from two-shears-like orbits, neutron (gd) orbits above Z = 50 shell and Z = 50, N = 50 core are investigated microscopically. The predicted B(E2), dynamic moment of inertia ℑ(2), deformation parameters β and γ, and ℑ(2)/B(E2) ratios in tilted axis cranking relativistic mean-field calculations are discussed and the characteristic features of antimagnetic rotation for the bands before and after alignment are shown. Supported by National Natural Science Foundation of China (11205068, 11205069, 11405072, 11475072, 11547308) and China Postdoctoral Science Foundation (2012M520667)
Nuclear Matter in Relativistic Mean Field Theory with Isovector Scalar Meson
Kubis, S
1997-01-01
Relativistic mean field (RMF) theory of nuclear matter with the isovector scalar mean field corresponding to the delta-meson [a_0(980)] is studied. While the delta-meson mean field vanishes in symmetric nuclear matter, it can influence properties of asymmetric nuclear matter in neutron stars. The RMF contribution due to delta-field to the nuclear symmetry energy is negative. To fit the empirical value, E_s=30 MeV, a stronger rho-meson coupling is required than in the absence of the delta-field. The energy per particle of neutron matter is then larger at high densities than the one with no delta-field included. Also, the proton fraction of beta-stable matter increases. Splitting of proton and neutron effective masses due to the delta-field can affect transport properties of neutron star matter.
MODEL STUDY OF THE SIGN PROBLEM IN A MEAN-FIELD APPROXIMATION.
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].
Nuclear matter EOS with light clusters within the mean-field approximation
Ferreira, Márcio
2013-01-01
The crust of a neutron star is essentially determined by the low-density region ($\\rho<\\rho_0\\approx0.15-0.16\\unit{fm}^{-3}$) of the equation of state. At the bottom of the inner crust, where the density is $\\rho\\lesssim0.1\\rho_0$, the formation of light clusters in nuclear matter will be energetically favorable at finite temperature. At very low densities and moderate temperatures, the few body correlations are expected to become important and light nuclei like deuterons, tritons, helions and $\\alpha$-particles will form. Due to Pauli blocking, these clusters will dissolve at higher densities $\\rho\\gtrsim 0.1\\rho_0$. The presence of these clusters influences the cooling process and quantities, such as the neutrino emissivity and gravitational waves emission. The dissolution density of these light clusters, treated as point-like particles, will be studied within the Relativistic Mean Field approximation. In particular, the dependence of the dissolution density on the clusters-meson couplings is studied.
Mean-field approximation for spacing distribution functions in classical systems
González, Diego Luis; Pimpinelli, Alberto; Einstein, T. L.
2012-01-01
We propose a mean-field method to calculate approximately the spacing distribution functions p(n)(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p(n)(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.
Neutron Stars in Relativistic Mean Field Theory with Isovector Scalar Meson
Kubis, S; Stachniewicz, S
1998-01-01
We study the equation of state of beta-stable dense matter and models of neutron stars in the relativistic mean field theory with the isovector scalar mean field corresponding to the delta-meson [a_0(980)]. A range of values of the delta-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, E_s=30 MeV. We find that the quantity most sensitive to the delta-meson coupling is the proton fraction of neutron star matter. It increases significantly in the presence of the delta-field. The energy per baryon also increases but the effect is smaller. The equation of state becomes slightly stiffer and the maximum neutron star mass increases for stronger delta-meson coupling.
Three-dimensional angular momentum projection in relativistic mean-field theory
Yao, J M; Ring, P; Arteaga, D Pena
2009-01-01
Based on a relativistic mean-field theory with an effective point coupling between the nucleons, three-dimensional angular momentum projection is implemented for the first time to project out states with designed angular momentum from deformed intrinsic states generated by triaxial quadrupole constraints. The same effective parameter set PC-F1 of the effective interaction is used for deriving the mean field and the collective Hamiltonian. Pairing correlations are taken into account by the BCS method using both monopole forces and zero range d-forces with strength parameters adjusted to experimental even-odd mass differences. The method is applied successfully to the isotopes 24Mg, 30Mg, and 32Mg.
Shell evolution at N=20 in the constrained relativistic mean field approach
无
2008-01-01
The shell evolution at N = 20, a disappearing neutron magic number observed experimentally in very neutron-rich nuclides, is investigated in the constrained relativistic mean field (RMF) theory. The trend of the shell closure observed experimentally towards the neutron drip-line can be reproduced. The predicted two-neutron separation energies, neutron shell gap energies and deformation parameters of ground states are shown as well. These results are compared with the recent Hartree-Fock-Bogliubov (HFB-14) model and the available experimental data. The perspective towards a better understanding of the shell evolution is discussed.
Fission Barrier for 240Pu in the Quadrupole Constrained Relativistic Mean Field Approach
L(U) Hong-Feng; GENG Li-Sheng; MENG Jie
2006-01-01
@@ The fission barrier for 240Pu is investigated beyond the second saddle point in the potential energy surface by the constrained relativistic mean field method with the newly proposed parameter set PK1. The microscopic correction for the centre-of-mass motion is essential to provide the correct potential energy surface. The shell effects that stabilize the nuclei against the fission is also investigated by the Strutinsky method. The shapes for the ground state, fission isomer and saddle-points, etc, are studied in detail.
Delta isobars in relativistic mean-field models with $\\sigma$-scaled hadron masses and couplings
Kolomeitsev, E E; Voskresensky, D N
2016-01-01
We extend the relativistic mean-field models with hadron masses and meson-baryon coupling constants dependent on the scalar $\\sigma$ field, studied previously to incorporate $\\Delta(1232)$ baryons. Available empirical information is analyzed to put constraints on the couplings of $\\Delta$s with meson fields. Conditions for the appearance of $\\Delta$s are studied. We demonstrate that with inclusion of the $\\Delta$s our equations of state continue to fulfill majority of known empirical constraints including the pressure-density constraint from heavy-ion collisions, the constraint on the maximum mass of the neutron stars, the direct Urca and the gravitational-baryon mass ratio constraints.
Pasta phases in neutron star studied with extended relativistic mean field models
Gupta, Neha
2013-01-01
To explain several properties of finite nuclei, infinite matter, and neutron stars in a unified way within the relativistic mean field models, it is important to extend them either with higher order couplings or with density-dependent couplings. These extensions are known to have strong impact in the high-density regime. Here we explore their role on the equation of state at densities lower than the saturation density of finite nuclei which govern the phase transitions associated with pasta structures in the crust of neutron stars.
Ground state properties of La isotopes in reflection asymmetric relativistic mean field theory
无
2009-01-01
The ground state properties of La isotopes are investigated with the reflection asymmetric relativistic mean field(RAS-RMF) model.The calculation results of binding energies and the quadrupole moments are in good agreements with the experiment.The calculation results indicate the change of the quadrupole deformation with the nuclear mass number.The "kink" on the isotope shifts is observed at A = 139 where the neutron number is the magic number N = 82.It is also found that the octupole deformations may exist in the La isotopes with mass number A ～ 145-155.
Ground state properties of La isotopes in reflection asymmetric relativistic mean field theory
WANG Nan; GUO Lu
2009-01-01
The ground state properties of La isotopes are investigated with the reflection asymmetric relativistic mean field (RAS-RMF) model.The calculation results of binding energies and the quadrupole moments are in good agreements with the experiment.The calculation results indicate the change of the quadrupole deformation with the nuclear mass number.The "kink" on the isotope shifts is observed at A=139 where the neutron number is the magic number N=82.It is also found that the octupole deformations may exist in the La isotopes with mass number A～ 145-155.
Tidal deformability of neutron and hyperon star with relativistic mean field equations of state
Kumar, Bharat; Patra, S K
2016-01-01
We systematically study the tidal deformability for neutron and hyperon stars using relativistic mean field (RMF) equations of state (EOSs). The tidal effect plays an important role during the early part of the evolution of compact binaries. Although, the deformability associated with the EOSs has a small correction, it gives a clean gravitational wave signature in binary inspiral. These are characterized by various love numbers kl (l=2, 3, 4), that depend on the EOS of a star for a given mass and radius. The tidal effect of star could be efficiently measured through advanced LIGO detector from the final stages of inspiraling binary neutron star (BNS) merger.
Proton and neutron skins of light nuclei within the Relativistic Mean Field theory
Geng, L S; Ozawa, A; Meng, J
2004-01-01
The Relativistic Mean Field (RMF) theory is applied to the analysis of ground-state properties of Ne, Na, Cl and Ar isotopes. In particular, we study the recently established proton skin in Ar isotopes and neutron skin in Na isotopes as a function of the difference between the proton and the neutron separation energy. We take the TMA effective interaction in the RMF Lagrangian, and describe pairing correlation by the density-independent delta-function interaction. We calculate single neutron and proton separation energies, quadrupole deformations, nuclear matter radii, and differences in proton radii and neutron radii, and compare these results with the recent experimental data.
Tidal deformability of neutron and hyperon stars within relativistic mean field equations of state
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.
Shell-model-like Approach (SLAP) for the Nuclear Properties in Relativistic Mean field Theory
MENG Jie; GUO Jian-you; LIU Lang; ZHANG Shuang-quan
2006-01-01
A Shell-model-like approach suggested to treat the pairing correlations in relativistic mean field theory is introduced,in which the occupancies thus obtained have been iterated back into the densities.The formalism and numerical techniques are given in detail.As examples,the ground state properties and low-lying excited states for Ne isotopes are studied.The results thus obtained are compared with the data available.The binding energies,the odd-even staggering,as well as the tendency for the change of the shapes in Ne isotopes are correctly reproduced.
Van Mieghem, P.F.A.; Van de Bovenkamp, R.
2015-01-01
Mean-field approximations (MFAs) are frequently used in physics. When a process (such as an epidemic or a synchronization) on a network is approximated by MFA, a major hurdle is the determination of those graphs for which MFA is reasonably accurate. Here, we present an accuracy criterion for Markovi
Multidimensionally constrained relativistic mean-field study of triple-humped barriers in actinides
Zhao, Jie; Lu, Bing-Nan; Vretenar, Dario; Zhao, En-Guang; Zhou, Shan-Gui
2015-01-01
Background: Potential energy surfaces (PES's) of actinide nuclei are characterized by a two-humped barrier structure. At large deformations beyond the second barrier, the occurrence of a third barrier was predicted by macroscopic-microscopic model calculations in the 1970s, but contradictory results were later reported by a number of studies that used different methods. Purpose: Triple-humped barriers in actinide nuclei are investigated in the framework of covariant density functional theory (CDFT). Methods: Calculations are performed using the multidimensionally constrained relativistic mean field (MDC-RMF) model, with the nonlinear point-coupling functional PC-PK1 and the density-dependent meson exchange functional DD-ME2 in the particle-hole channel. Pairing correlations are treated in the BCS approximation with a separable pairing force of finite range. Results: Two-dimensional PES's of 226,228,230,232Th and 232,235,236,238U are mapped and the third minima on these surfaces are located. Then one-dimensional potential energy curves along the fission path are analyzed in detail and the energies of the second barrier, the third minimum, and the third barrier are determined. The functional DD-ME2 predicts the occurrence of a third barrier in all Th nuclei and 238U . The third minima in 230 ,232Th are very shallow, whereas those in 226 ,228Th and 238U are quite prominent. With the functional PC-PK1 a third barrier is found only in 226 ,228 ,230Th . Single-nucleon levels around the Fermi surface are analyzed in 226Th, and it is found that the formation of the third minimum is mainly due to the Z =90 proton energy gap at β20≈1.5 and β30≈0.7 . Conclusions: The possible occurrence of a third barrier on the PES's of actinide nuclei depends on the effective interaction used in multidimensional CDFT calculations. More pronounced minima are predicted by the DD-ME2 functional, as compared to the functional PC-PK1. The depth of the third well in Th isotopes decreases
Typel, S.; Wolter, H.H. [Sektion Physik, Univ. Muenchen, Garching (Germany)
1998-06-01
Nuclear matter and ground state properties for (proton and neutron) semi-closed shell nuclei are described in relativistic mean field theory with coupling constants which depend on the vector density. The parametrization of the density dependence for {sigma}-, {omega}- and {rho}-mesons is obtained by fitting to properties of nuclear matter and some finite nuclei. The equation of state for symmetric and asymmetric nuclear matter is discussed. Finite nuclei are described in Hartree approximation, including a charge and an improved center-of-mass correction. Pairing is considered in the BCS approximation. Special attention is directed to the predictions for properties at the neutron and proton driplines, e.g. for separation energies, spin-orbit splittings and density distributions. (orig.)
New parameterization of the effective field theory motivated relativistic mean field model
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.
Hyperons in neutron star matter within relativistic mean-field models
Oertel, M; Gulminelli, F; Raduta, A R
2014-01-01
Since the discovery of neutron stars with masses around 2 solar masses the composition of matter in the central part of these massive stars has been intensively discussed. Within this paper we will (re)investigate the question of the appearance of hyperons. To that end we will perform an extensive parameter study within relativistic mean field models. We will show that it is possible to obtain high mass neutron stars (i) with a substantial amount of hyperons, (ii) radii of 12-13 km for the canonical mass of 1.4 solar masses, and (iii) a spinodal instability at the onset of hyperons. The results depend strongly on the interaction in the hyperon-hyperon channels, on which only very little information is available from terrestrial experiments up to now.
B-Spline Finite Elements and their Efficiency in Solving Relativistic Mean Field Equations
Pöschl, W
1997-01-01
A finite element method using B-splines is presented and compared with a conventional finite element method of Lagrangian type. The efficiency of both methods has been investigated at the example of a coupled non-linear system of Dirac eigenvalue equations and inhomogeneous Klein-Gordon equations which describe a nuclear system in the framework of relativistic mean field theory. Although, FEM has been applied with great success in nuclear RMF recently, a well known problem is the appearance of spurious solutions in the spectra of the Dirac equation. The question, whether B-splines lead to a reduction of spurious solutions is analyzed. Numerical expenses, precision and behavior of convergence are compared for both methods in view of their use in large scale computation on FEM grids with more dimensions. A B-spline version of the object oriented C++ code for spherical nuclei has been used for this investigation.
Description of 178 Hfm2 in the Constrained Relativistic Mean Field Theory
ZHANG Wei; PENG Jing; ZHANG Shuang-Quan
2009-01-01
Properties of the ground state of 178 Hf and the isomeric state 178Hfn2 are studied within the adiabatic and diabatic constrained relativistic mean field (RMF) approaches. The RMF calculations reproduce well the binding energy and the deformation for the ground state of 178Hf. Using the ground state single-particle eigenvalues obtained in the present calculation, the lowest excitation configuration with Kπ = 16+ is found to be v(7/2- [514])-1 (9/2+ [624])1 π(7/2+ [404])-1 (9/2-[514])1. Its excitation energy calculated by the RMF theory with time-odd fields taken into account is equal to 2.801 MeV, i.e., close to the 178 Hfm2 experimental excitation energy 2.446 MeV. The self-consistent procedure accounting for the time-odd component of the meson fields is the most important aspect of the present calculation.
Study of reaction and decay using densities from relativistic mean field theory
Gangopadhyay, G
2012-01-01
Relativistic mean field calculations have been performed to obtain nuclear density pro- file. Microscopic interactions have been folded with the calculated densities of finite nuclei to obtain a semi-microscopic potential. Life time values for the emission of proton, alpha particles and complex clusters have been calculated in the WKB approach assum- ing a tunneling process through the potential barrier. Elastic scattering cross sections have been estimated for proton-nucleus scattering in light neutron rich nuclei. Low en- ergy proton reactions have been studied and their astrophysical implications have been discussed. The success of the semi-microscopic potentials obtained in the folding model with RMF densities in explaining nuclear decays and reactions has been emphasized.
Ground-State Properties of Z = 59 Nuclei in the Relativistic Mean-Field Theory
ZHOU Yong; MA Zhong-Yu; CHEN Bao-Qiu; LI Jun-Qing
2000-01-01
Ground-state properties of Pr isotopes are studied in a framework of the relativistic mean-field (RMF) theory using the recently proposed parameter set TM1. Bardeen-Cooper-Schrieffer (BCS) pproximation and blocking method is adopted to deal with pairing interaction and the odd nucleon, respectively. The pairing forces are taken to be isospin dependent. The domain of the validity of the BCS theory and the positions of neutron and proton drip lines are studied. It is shown that RMF theory has provided a good description of the binding energy,isotope shifts and deformation of nuclei over a large range of Pr isotopes, which are in good agreement with those obtained in the finite-range droplet model.
Investigation of A＋c- and Ab-Hypernuclei in Relativistic Mean-Field Model
TANYu-Hong; CAIChong-Hai; LILei; NINGPing-Zhi
2003-01-01
We investigate the properties of A+c- and Ab-hypernuclei within the framework of the relativistic mean-field model (RMF). It is found that no A+c bound states can exist if the A+c potential well depth |UA+c| in nuclear matter is less than 10 MeV. If |UA+c|is less than 20 MeV, A+c cannot bind to the heavier nuclei with atomic number larger than 100. We suggest it is preferable to search the A+c-hypernuclei from medium-heavy nuclear systems in experiment. Very small spin-orbit splitting for the A+c in hypernuclei is a/so observed, and for the Ab it is nearly zero.
Magnetic moments of 33Mg in the time-odd relativistic mean field approach
无
2009-01-01
The configuration-fixed deformation constrained relativistic mean field approach with time-odd component has been applied to investigate the ground state properties of 33Mg with effective interaction PK1.The ground state of 33Mg has been found to be prolate deformed,β2=0.23,with the odd neutron in 1/2[330] orbital and the energy -251.85 MeV which is close to the data -252.06 MeV.The magnetic moment -0.9134 μN is obtained with the effective electromagnetic current which well reproduces the data -0.7456 μN self-consistently without introducing any parameter.The energy splittings of time reversal conjugate states,the neutron current,the energy contribution from the nuclear magnetic potential,and the effect of core polarization are discussed in detail.
K--nucleus relativistic mean field potentials consistent with kaonic atoms
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.
Simplified method for including spatial correlations in mean-field approximations
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.
Mean-field approximation for the potts model of a diluted magnet in the external field
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.
Sulaksono, A; Agrawal, B K
2014-01-01
The model dependence and the symmetry energy dependence of the core-crust transition properties for the neutron stars are studied using three different families of systematically varied extended relativistic mean field model. Several forces within each of the families are so considered that they yield wide variations in the values of the nuclear symmetry energy $a_{\\rm sym}$ and its slope parameter $L$ at the saturation density. The core-crust transition density is calculated using a method based on random-phase-approximation. The core-crust transition density is strongly correlated, in a model independent manner, with the symmetry energy slope parameter evaluated at the saturation density. The pressure at the transition point dose not show any meaningful correlations with the symmetry energy parameters at the saturation density. At best, pressure at the transition point is correlated with the symmetry energy parameters and their linear combination evaluated at the some sub-saturation density. Yet, such corre...
Zhao, Jie; Niksic, Tamara; Vretenar, Dario; Zhou, Shan-Gui
2016-01-01
Studies of fission dynamics, based on nuclear energy density functionals, have shown that the coupling between shape and pairing degrees of freedom has a pronounced effect on the nonperturbative collective inertia and, therefore, on dynamic (least-action) spontaneous fission paths and half-lives. Collective potentials and nonperturbative cranking collective inertia tensors are calculated using the multidimensionally-constrained relativistic mean-field (MDC-RMF) model. Pairing correlations are treated in the BCS approximation using a separable pairing force of finite range. Pairing fluctuations are included as a collective variable using a constraint on particle-number dispersion. Fission paths are determined with the dynamic programming method by minimizing the action in multidimensional collective spaces. The dynamics of spontaneous fission of $^{264}$Fm and $^{250}$Fm are explored. Fission paths, action integrals and corresponding half-lives computed in the three-dimensional collective space of shape and pa...
Treating Coulomb exchange contributions in relativistic mean field calculations: why and how
Van Giai, Nguyen; Gu, Huai-Qiang; Long, Wenhui; Meng, Jie
2014-01-01
The energy density functional (EDF) method is very widely used in nuclear physics, and among the various existing functionals those based on the relativistic Hartree (RH) approximation are very popular because the exchange contributions (Fock terms) are numerically rather onerous to calculate. Although it is possible to somehow 'mock up' the effects of meson-induced exchange terms by adjusting the meson-nucleon couplings, the lack of Coulomb exchange contributions hampers the accuracy of predictions. In this note, we show that the Coulomb exchange effects can be easily included with a good accuracy in a perturbative approach. Therefore, it would be desirable for future relativistic EDF models to incorporate Coulomb exchange effects, at least to some order of perturbation.
Parity Violating Electron Scattering in the Relativistic Eikonal Approximation
DONG Tie-Kuang; REN Zhong-Zhou
2008-01-01
The parity violating electron scattering is investigated in the relativistic Eikonal approximation. The parity violating asymmetry parameters for many isotopes are calculated. In calculations the proton and neutron densities are obtained from the relativistic mean-field theory. We take Ni isotopes as examples to analyse the behaviour of the parity violating asymmetry parameters. The results show that the parity violating asymmetry parameter is sensitive to the difference between the proton and neutron densities. The amplitude of the parity violating asymmetry parameter increases with the distance between the minima of proton and neutron form factors. Our results are useful for future parity violating electron scattering experiments. By comparing our results with experimental data one can test the validity of the relativistic mean-field theory in calculating the neutron densities of nuclei.
Particle-number projection in the finite-temperature mean-field approximation
Fanto, P; Bertsch, G F
2016-01-01
Calculation of statistical properties of nuclei in a finite-temperature mean-field theory requires projection onto good particle number, since the theory is formulated in the grand canonical ensemble. This projection is usually carried out in a saddle-point approximation. Here we derive formulas for an exact particle-number projection of the finite-temperature mean-field solution. We consider both deformed nuclei, in which the pairing condensate is weak and the Hartree-Fock (HF) approximation is the appropriate mean-field theory, and nuclei with strong pairing condensates, in which the appropriate theory is the Hartree-Fock-Bogoliubov (HFB) approximation, a method that explicitly violates particle-number conservation. For the HFB approximation, we present a general projection formula for a condensate that is time-reversal invariant and a simpler formula for the Bardeen-Cooper-Schrieffer (BCS) limit, which is realized in nuclei with spherical condensates. We apply the method to three heavy nuclei: a typical de...
Merging Belief Propagation and the Mean Field Approximation: A Free Energy Approach
Riegler, Erwin; Kirkelund, Gunvor Elisabeth; Manchón, Carles Navarro
2013-01-01
We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al. We show that the message passing fixed-point equations obtained with this combination...... correspond to stationary points of a constrained region-based free energy approximation. Moreover, we present a convergent implementation of these message passing fixed-point equations provided that the underlying factor graph fulfills certain technical conditions. In addition, we show how to include hard...
Madokoro, Hideki; Matsuzaki, Masayuki
1997-01-01
Relativistic Mean Field Theory is applied to the description of rotating nuclei. Since the previous formulation of Munich group was based on a special relativistic transformation property of the spinor fields, we reformulate in a fully covariant manner using tetrad formalism. The numerical calculations are performed for 3 zinc isotopes, including the newly discovered superdeformed band in $^{62}$Zn which is the first experimental observation in this mass region.
Madokoro, H.; Matsuzaki, M.
Relativistic Mean Field Theory is applied to the description of rotating nuclei. Since the previous formulation of Munich group was based on a special relativistic transformation property of the spinor fields, we reformulate in a fully covariant manner using tetrad formalism. The numerical calculations are performed for 3 zinc isotopes, including the newly discovered superdeformed band in $^{62}$Zn which is the first experimental observation in this mass region.
A Study of Multi-Λ Hypernuclei Within Spherical Relativistic Mean-Field Approach
Rather, Asloob A.; Ikram, M.; Usmani, A. A.; Kumar, B.; Patra, S. K.
2017-09-01
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
Nucleon Finite Volume Effect and Nuclear Matter Properties in a Relativistic Mean-Field Theory
R. Costa; A.J. Santiago; H. Rodrigues; J. Sa Borges
2006-01-01
Effects of excluded volume of nucleons on nuclear matter are studied, and the nuclear properties that follow from different relativistic mean-field model parametrizations are compared. We show that, for all tested parametrizations,the resulting volume energy a1 and the symmetry energy J are around the acceptable values of 16 MeV and 30 MeV,and the density symmetry L is around 100 Me V. On the other hand, models that consider only linear terms lead to incompressibility K0 much higher than expected. For most parameter sets there exists a critical point (ρc,δc), where the minimum and the maximum of the equation of state are coincident and the incompressibility equals zero. This critical point depends on the excluded volume parameter r. If this parameter is larger than 0.5 fm, there is no critical point and the pure neutron matter is predicted to be bound. The maximum value for neutron star mass is 1.85M⊙, which is in agreement with the mass of the heaviest observed neutron star 4U0900-40 and corresponds to r = 0.72 fm. We also show that the light neutron star mass (1.2M⊙) is obtained for r (≌) 0.9 fm.
A Second Relativistic Mean Field and Virial Equation of State for Astrophysical Simulations
Shen, G; O'Connor, E
2011-01-01
We generate a second equation of state (EOS) of nuclear matter for a wide range of temperatures, densities, and proton fractions for use in supernovae, neutron star mergers, and black hole formation simulations. We employ full relativistic mean field (RMF) calculations for matter at intermediate density and high density, and the Virial expansion of a non-ideal gas for matter at low density. For this EOS we use the RMF effective interaction FSUGold, whereas our earlier EOS was based on the RMF effective interaction NL3. The FSUGold interaction has a lower pressure at high densities compared to the NL3 interaction. We calculate the resulting EOS at over 100,000 grid points in the temperature range $T$ = 0 to 80 MeV, the density range $n_B$ = 10$^{-8}$ to 1.6 fm$^{-3}$, and the proton fraction range $Y_p$ = 0 to 0.56. We then interpolate these data points using a suitable scheme to generate a thermodynamically consistent equation of state table on a finer grid. We discuss differences between this EOS, our NL3 ba...
Lu, Bing-Nan; Zhao, En-Guang; Zhou, Shan-Gui
2013-01-01
In this contribution we present some results of potential energy surfaces of actinide and transfermium nuclei from multi-dimensional constrained relativistic mean field (MDC-RMF) models. Recently we developed multi-dimensional constrained covariant density functional theories (MDC-CDFT) in which all shape degrees of freedom $\\beta_{\\lambda\\mu}$ with even $\\mu$ are allowed and the functional can be one of the following four forms: the meson exchange or point-coupling nucleon interactions combined with the non-linear or density-dependent couplings. In MDC-RMF models, the pairing correlations are treated with the BCS method. With MDC-RMF models, the potential energy surfaces of even-even actinide nuclei were investigated and the effect of triaxiality on the fission barriers in these nuclei was discussed. The non-axial reflection-asymmetric $\\beta_{32}$ shape in some transfermium nuclei with $N=150$, namely $^{246}$Cm, $^{248}$Cf, $^{250}$Fm, and $^{252}$No were also studied.
Mean-Field Approximation to the Hydrophobic Hydration in the Liquid-Vapor Interface of Water.
Abe, Kiharu; Sumi, Tomonari; Koga, Kenichiro
2016-03-03
A mean-field approximation to the solvation of nonpolar solutes in the liquid-vapor interface of aqueous solutions is proposed. It is first remarked with a numerical illustration that the solvation of a methane-like solute in bulk liquid water is accurately described by the mean-field theory of liquids, the main idea of which is that the probability (Pcav) of finding a cavity in the solvent that can accommodate the solute molecule and the attractive interaction energy (uatt) that the solute would feel if it is inserted in such a cavity are both functions of the solvent density alone. It is then assumed that the basic idea is still valid in the liquid-vapor interface, but Pcav and uatt are separately functions of different coarse-grained local densities, not functions of a common local density. Validity of the assumptions is confirmed for the solvation of the methane-like particle in the interface of model water at temperatures between 253 and 613 K. With the mean-field approximation extended to the inhomogeneous system the local solubility profiles across the interface at various temperatures are calculated from Pcav and uatt obtained at a single temperature. The predicted profiles are in excellent agreement with those obtained by the direct calculation of the excess chemical potential over an interfacial region where the solvent local density varies most rapidly.
Maslov, K A; Voskresensky, D N
2016-01-01
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 $\\Delta$ 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 $\\Delta$ isobars. We analyze available empirical information to put constraints on coupling constants of $\\Delta$s to mesonic mean fields. We show that the resulting equation of state satisfies majority of presently known experimental constraints.
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
Mean-field approximation for the Sznajd model in complex networks
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.
On the connections and differences among three mean-field approximations: a stringent test.
Yi, Shasha; Pan, Cong; Hu, Liming; Hu, Zhonghan
2017-07-19
This letter attempts to clarify the meaning of three closely related mean-field approximations: random phase approximation (RPA), local molecular field (LMF) approximation, and symmetry-preserving mean-field (SPMF) approximation, and their use of reliability and validity in the field of theory and simulation of liquids when the long-ranged component of the intermolecular interaction plays an important role in determining density fluctuations and correlations. The RPA in the framework of classical density functional theory (DFT) neglects the higher order correlations in the bulk and directly applies the long-ranged part of the potential to correct the pair direct correlation function of the short-ranged system while the LMF approach introduces a nonuniform mimic system under a reconstructed static external potential that accounts for the average effect arising from the long-ranged component of the interaction. Furthermore, the SPMF approximation takes the viewpoint of LMF but instead instantaneously averages the long-ranged component of the potential over the degrees of freedom in the direction with preserved symmetry. The formal connections and the particular differences of the viewpoint among the three approximations are explained and their performances in producing structural properties of liquids are stringently tested using an exactly solvable model. We demonstrate that the RPA treatment often yields uncontrolled poor results for pair distribution functions of the bulk system. On the other hand, the LMF theory produces quite reasonably structural correlations when the pair distribution in the bulk is converted to the singlet particle distribution in the nonuniform system. It turns out that the SPMF approach outperforms the other two at all densities and under extreme conditions where the long-ranged component significantly contributes to the structural correlations.
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.
Continuum theory of critical phenomena in polymer solutions: Formalism and mean field approximation
Goldstein, Raymond E.; Cherayil, Binny J.
1989-06-01
A theoretical description of the critical point of a polymer solution is formulated directly from the Edwards continuum model of polymers with two- and three-body excluded-volume interactions. A Hubbard-Stratonovich transformation analogous to that used in recent work on the liquid-vapor critical point of simple fluids is used to recast the grand partition function of the polymer solution as a functional integral over continuous fields. The resulting Landau-Ginzburg-Wilson (LGW) Hamiltonian is of the form of a generalized nonsymmetric n=1 component vector model, with operators directly related to certain connected correlation functions of a reference system. The latter is taken to be an ensemble of Gaussian chains with three-body excluded-volume repulsions, and the operators are computed in three dimensions by means of a perturbation theory that is rapidly convergent for long chains. A mean field theory of the functional integral yields a description of the critical point in which the power-law variations of the critical polymer volume fraction φc, critical temperature Tc, and critical amplitudes on polymerization index N are essentially identical to those found in the Flory-Huggins theory. In particular, we find φc ˜N-1/2, Tθ-Tc˜N-1/2 with (Tθ the theta temperature), and that the composition difference between coexisting phases varies with reduced temperature t as N-1/4t1/2. The mean field theory of the interfacial tension σ between coexisting phases near the critical point, developed by considering the LGW Hamiltonian for a weakly inhomogeneous solution, yields σ˜N-1/4t3/2, with the correlation length diverging as ξ˜N1/4t-1/2 within the same approximation, consistent with the mean field limit of de Gennes' scaling form. Generalizations to polydisperse systems are discussed.
A systematic sequence of relativistic approximations.
Dyall, Kenneth G
2002-06-01
An approach to the development of a systematic sequence of relativistic approximations is reviewed. The approach depends on the atomically localized nature of relativistic effects, and is based on the normalized elimination of the small component in the matrix modified Dirac equation. Errors in the approximations are assessed relative to four-component Dirac-Hartree-Fock calculations or other reference points. Projection onto the positive energy states of the isolated atoms provides an approximation in which the energy-dependent parts of the matrices can be evaluated in separate atomic calculations and implemented in terms of two sets of contraction coefficients. The errors in this approximation are extremely small, of the order of 0.001 pm in bond lengths and tens of microhartrees in absolute energies. From this approximation it is possible to partition the atoms into relativistic and nonrelativistic groups and to treat the latter with the standard operators of nonrelativistic quantum mechanics. This partitioning is shared with the relativistic effective core potential approximation. For atoms in the second period, errors in the approximation are of the order of a few hundredths of a picometer in bond lengths and less than 1 kJ mol(-1) in dissociation energies; for atoms in the third period, errors are a few tenths of a picometer and a few kilojoule/mole, respectively. A third approximation for scalar relativistic effects replaces the relativistic two-electron integrals with the nonrelativistic integrals evaluated with the atomic Foldy-Wouthuysen coefficients as contraction coefficients. It is similar to the Douglas-Kroll-Hess approximation, and is accurate to about 0.1 pm and a few tenths of a kilojoule/mole. The integrals in all the approximations are no more complicated than the integrals in the full relativistic methods, and their derivatives are correspondingly easy to formulate and evaluate.
Mean field approximation for biased diffusion on Japanese inter-firm trading network.
Watanabe, Hayafumi
2014-01-01
By analysing the financial data of firms across Japan, a nonlinear power law with an exponent of 1.3 was observed between the number of business partners (i.e. the degree of the inter-firm trading network) and sales. In a previous study using numerical simulations, we found that this scaling can be explained by both the money-transport model, where a firm (i.e. customer) distributes money to its out-edges (suppliers) in proportion to the in-degree of destinations, and by the correlations among the Japanese inter-firm trading network. However, in this previous study, we could not specifically identify what types of structure properties (or correlations) of the network determine the 1.3 exponent. In the present study, we more clearly elucidate the relationship between this nonlinear scaling and the network structure by applying mean-field approximation of the diffusion in a complex network to this money-transport model. Using theoretical analysis, we obtained the mean-field solution of the model and found that, in the case of the Japanese firms, the scaling exponent of 1.3 can be determined from the power law of the average degree of the nearest neighbours of the network with an exponent of -0.7.
Study of the Alpha-Decay Chain for7753 194Rn with Relativistic Mean-Field Theory
SHENG Zong-Qiang; GUO Jian-You
2008-01-01
The structures of the nuclei on the alpha-decay chain of 194Rn are investigated in the deformed relativistic mean-field theory with the effective interaction TMA. We put an emphasis on the ground state properties of 194Rn. The calculated alpha-decay energies and lifetimes are both very close to the experimental data for 186pb and 190po. For 194 Rn, the deviations are a little large on both the alpha-decay energy and the lifetime. We also calculate the alpha-decay energies for the isotopes 192～208Rn. The tendency for the change of the alpha-decay energies with neutron number is correctly reproduced in the relativistic mean-field theory (RMF). In general, the RMF theory can give a good description of the alpha decay chain of 194Rn.
Pietracaprina, Francesca; Ros, Valentina; Scardicchio, Antonello
2016-02-01
In this paper we analyze the predictions of the forward approximation in some models which exhibit an Anderson (single-body) or many-body localized phase. This approximation, which consists of summing over the amplitudes of only the shortest paths in the locator expansion, is known to overestimate the critical value of the disorder which determines the onset of the localized phase. Nevertheless, the results provided by the approximation become more and more accurate as the local coordination (dimensionality) of the graph, defined by the hopping matrix, is made larger. In this sense, the forward approximation can be regarded as a mean-field theory for the Anderson transition in infinite dimensions. The sum can be efficiently computed using transfer matrix techniques, and the results are compared with the most precise exact diagonalization results available. For the Anderson problem, we find a critical value of the disorder which is 0.9 % off the most precise available numerical value already in 5 spatial dimensions, while for the many-body localized phase of the Heisenberg model with random fields the critical disorder hc=4.0 ±0.3 is strikingly close to the most recent results obtained by exact diagonalization. In both cases we obtain a critical exponent ν =1 . In the Anderson case, the latter does not show dependence on the dimensionality, as it is common within mean-field approximations. We discuss the relevance of the correlations between the shortest paths for both the single- and many-body problems, and comment on the connections of our results with the problem of directed polymers in random medium.
Beyond-mean-field corrections within the second random-phase approximation
Grasso, M.; Gambacurta, D.; Engel, J.
2016-06-01
A subtraction procedure, introduced to overcome double-counting problems in beyond-mean-field theories, is used in the second random-phase approximation (SRPA). Doublecounting problems arise in the energy-density functional framework in all cases where effective interactions tailored at leading order are used for higher-order calculations, such as those done in the SRPA model. It was recently shown that this subtraction procedure also guarantees that the stability condition related to the Thouless theorem is verified in extended RPA models. We discuss applications of the subtraction procedure, introduced within the SRPA model, to the nucleus 16O. The application of the subtraction procedure leads to: (i) stable results that are weakly cutoff dependent; (ii) a considerable upwards correction of the SRPA spectra (which were systematically shifted downwards by several MeV with respect to RPA spectra, in all previous calculations). With this important implementation of the model, many applications may be foreseen to analyze the genuine impact of 2 particle-2 hole configurations (without any cutoff dependences and anomalous shifts) on the excitation spectra of medium-mass and heavy nuclei.
Geng, L S; Meng, J
2005-01-01
We perform a systematic study of the ground-state properties of all the nuclei from the proton drip line to the neutron drip line throughout the periodic table employing the relativistic mean field model. The TMA parameter set is used for the mean-field Lagrangian density, and a state-dependent BCS method is adopted to describe the pairing correlation. The ground-state properties of a total of 6969 nuclei with $Z,N\\ge 8$ and $Z\\le 100$ from the proton drip line to the neutron drip line, including the binding energies, the separation energies, the deformations, and the rms charge radii, are calculated and compared with existing experimental data and those of the FRDM and HFB-2 mass formulae. This study provides the first complete picture of the current status of the descriptions of nuclear ground-state properties in the relativistic mean field model. The deviations from existing experimental data indicate either that new degrees of freedom are needed, such as triaxial deformations, or that serious effort is ne...
Mean-field effects on flows in relativistic heavy-ion collisions
Isse, M.; Ohnishi, A. [Hokkaido Univ., Graduate School of Science, Sapporo, Hokkaido (Japan); Otuka, N. [Hokkaido Univ., Graduate School of Engineering, Sapporo, Hokkaido (Japan); Sahu, P.K. [Istituto Nazionale di Fisica Nucleare, Sezione di Catania (Italy); Nara, Y. [Brookhaven National Laboratory, RIKEN BNL Research Center, Upton, NY (United States)
2002-09-01
At RHIC experiments, started in 2000, the data obtained recently seem to exhibit QGP formation, but the conclusion is not drawn yet. Here, we pay out attention to the collective flows at hadronic freeze-out as an evidence of QGP formation. To discuss it, the mean-field effect on the flows is not negligible. It is dominant at SIS or AGS energy, and our conjecture is that it is negligible at SPS or RHIC energy. We formed a model to investigate our assumption, and some simulated results are shown. (author)
Building relativistic mean field models for finite nuclei and neutron stars
Chen, Wei-Chia; Piekarewicz, J.
2014-10-01
Background: Theoretical approaches based on density functional theory provide the only tractable method to incorporate the wide range of densities and isospin asymmetries required to describe finite nuclei, infinite nuclear matter, and neutron stars. Purpose: A relativistic energy density functional (EDF) is developed to address the complexity of such diverse nuclear systems. Moreover, a statistical perspective is adopted to describe the information content of various physical observables. Methods: We implement the model optimization by minimizing a suitably constructed χ2 objective function using various properties of finite nuclei and neutron stars. The minimization is then supplemented by a covariance analysis that includes both uncertainty estimates and correlation coefficients. Results: A new model, "FSUGold2," is created that can well reproduce the ground-state properties of finite nuclei, their monopole response, and that accounts for the maximum neutron-star mass observed up to date. In particular, the model predicts both a stiff symmetry energy and a soft equation of state for symmetric nuclear matter, suggesting a fairly large neutron-skin thickness in Pb208 and a moderate value of the nuclear incompressibility. Conclusions: We conclude that without any meaningful constraint on the isovector sector, relativistic EDFs will continue to predict significantly large neutron skins. However, the calibration scheme adopted here is flexible enough to create models with different assumptions on various observables. Such a scheme—properly supplemented by a covariance analysis—provides a powerful tool to identify the critical measurements required to place meaningful constraints on theoretical models.
Building relativistic mean field models for finite nuclei and neutron stars
Chen, Wei-Chia
2014-01-01
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 chi-square 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 particul...
Nonuniversal behavior for aperiodic interactions within a mean-field approximation.
Faria, Maicon S; Branco, N S; Tragtenberg, M H R
2008-04-01
We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following one of two deterministic aperiodic sequences, the Fibonacci or period-doubling one. New algorithms of sequence generation were implemented, which were fundamental in obtaining long sequences and, therefore, precise results. We calculate the exact critical temperature for both sequences, as well as the critical exponents beta, gamma, and delta . For the Fibonacci sequence, the exponents are classical, while for the period-doubling one they depend on the ratio between the two exchange constants. The usual relations between critical exponents are satisfied, within error bars, for the period-doubling sequence. Therefore, we show that mean-field-like procedures may lead to nonclassical critical exponents.
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.
CHEN Jin-Gen; ZHOU Xing-Fei; WANG Kun; MA Guo-Liang; TIAN Wen-Dong; ZUO Jia-Xu; MA Chun-Wang; CHEN Jin-Hui; YAN Ting-Zhi; SHEN Wen-Qing; CAI Xiang-Zhou; WANG Ting-Tai; MA Yu-Gang; REN Zhong-Zhou; FANG De-Qing; ZHONG Chen; WEI Yi-Bin; GUO Wei
2004-01-01
@@ A candidate for proton halo nucleus 23Al is investigated based on the constrained calculations in the framework of the deformed relativistic mean field (RMF) model with the NL075 parameter set. It is shown by the constrained calculations that the ground state of 23Al has a large deformation that corresponds to the prolate shape. With that large deformation, the non-constrained RMF calculation predicts that there appears an inversion between the 2s1/2 [211] and 1d5/2 [202] shells. The valence proton of 23Al is weakly bound and occupies 2s1/2 [211] and 1d5/2 [202] with the weights of 56% and 29%, respectively. The calculated RMS radius for matter is in agreement with the experimental one. It is also predicted that the difference between the proton RMS radius and the neutron one is very large. This suggests that there exists a proton halo in 23Al.
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)
Afanasjev, A. V.; König, J.; Ring, P.
1996-02-01
The cranked relativistic mean field approach is applied for a systematic investigation of superdeformed rotational bands observed in the A ˜ 140-150 mass region. The present investigation covers yrast and in some cases also excited superdeformed bands of all nuclei of this mass region in which such bands have been observed so far. Using the parameter set NL1, which has been adjusted ten years ago to a few spherical nuclei, reasonable agreement with experimental data is obtained throughout the mass region under investigation. It is shown that the calculated properties of superdeformed rotational bands such as the dependence of the dynamic moment of inertia J(2) with respect to the rotational frequency and the absolute value of the charge quadrupole moment Q0 depends sensitively on the number of occupied high- N intruder orbitals. This is agreement both with previous investigations within the cranked Nilsson-Strutinsky and the cranked Woods-Saxon-Strutinsky approaches and with available experimental data.
Relativistic continuum random phase approximation in spherical nuclei
Daoutidis, Ioannis
2009-10-01
Covariant density functional theory is used to analyze the nuclear response in the external multipole fields. The investigations are based on modern functionals with zero range and density dependent coupling constants. After a self-consistent solution of the Relativistic Mean Field (RMF) equations for the nuclear ground states multipole giant resonances are studied within the Relativistic Random Phase Approximation (RRPA), the small amplitude limit of the time-dependent RMF. The coupling to the continuum is treated precisely by calculating the single particle Greens-function of the corresponding Dirac equation. In conventional methods based on a discretization of the continuum this was not possible. The residual interaction is derived from the same RMF Lagrangian. This guarantees current conservation and a precise decoupling of the Goldstone modes. For nuclei with open shells pairing correlations are taken into account in the framework of BCS theory and relativistic quasiparticle RPA. Continuum RPA (CRPA) presents a robust method connected with an astonishing reduction of the numerical effort as compared to conventional methods. Modes of various multipolarities and isospin are investigated, in particular also the newly discovered Pygmy modes in the vicinity of the neutron evaporation threshold. The results are compared with conventional discrete RPA calculations as well as with experimental data. We find that the full treatment of the continuum is essential for light nuclei and the study of resonances in the neighborhood of the threshold. (orig.)
Quantum Dynamics of Dark and Dark-Bright Solitons beyond the Mean-Field Approximation
Krönke, Sven; Schmelcher, Peter
2014-05-01
Dark solitons are well-known excitations in one-dimensional repulsively interacting Bose-Einstein condensates, which feature a characteristical phase-jump across a density dip and form stability in the course of their dynamics. While these objects are stable within the celebrated Gross-Pitaevskii mean-field theory, the situation changes dramatically in the full many-body description: The condensate being initially in a dark soliton state dynamically depletes and the density notch fills up with depleted atoms. We analyze this process in detail with a particular focus on two-body correlations and the fate of grey solitons (dark solitons with finite density in the notch) and thereby complement the existing results in the literature. Moreover, we extend these studies to mixtures of two repulsively interacting bosonic species with a dark-bright soliton (dark soliton in one component filled with localized atoms of the other component) as the initial state. All these many-body quantum dynamics simulations are carried out with the recently developed multi-layer multi-configuration time-dependent Hartree method for bosons (ML-MCTDHB).
Thermal vacancies in random alloys in the single-site mean-field approximation
Ruban, A. V.
2016-04-01
A formalism for the vacancy formation energies in random alloys within the single-site mean-filed approximation, where vacancy-vacancy interaction is neglected, is outlined. It is shown that the alloy configurational entropy can substantially reduce the concentration of vacancies at high temperatures. The energetics of vacancies in random Cu0.5Ni0.5 alloy is considered as a numerical example illustrating the developed formalism. It is shown that the effective formation energy increases with temperature, however, in this particular system it is still below the mean value of the vacancy formation energy, which would correspond to the vacancy formation energy in a homogeneous model of a random alloy, such as given by the coherent potential approximation.
Opper, Manfred; Winther, Ole
2001-01-01
We develop an advanced mean held method for approximating averages in probabilistic data models that is based on the Thouless-Anderson-Palmer (TAP) approach of disorder physics. In contrast to conventional TAP. where the knowledge of the distribution of couplings between the random variables is r...... is required. our method adapts to the concrete couplings. We demonstrate the validity of our approach, which is so far restricted to models with nonglassy behavior? by replica calculations for a wide class of models as well as by simulations for a real data set....
Thermal vacancies in random alloys in the single-site mean-field approximation
Ruban, Andrei V
2015-01-01
A formalism for the vacancy formation energies in random alloys is outlined within the single-site mean-filed approximation where vacancy-vacancy interaction is neglected. It is shown that alloy entropy (without vacancies) can substantially reduce the concentration of vacancies at high temperatures. The energetics of vacancies in random Cu_0.5Ni_0.5 alloy is considered as a numerical example illustrating the developed formalism. It is shown that the effective formation energy is increases with temperature, however, in this particular system it is still below the mean value of the vacancy formation energy due to a large dispersion of the local vacancy formation energies.
Afanasjev, A.V. [Technische Univ. Muenchen, Garching (Germany). Physik-Department]|[Latvian Acad. of Sci., Salaspils (Latvia). Dept. of Math. Phys.]|[Lund Inst. of Tech. (Sweden). Dept. of Mathematical Physics; Koenig, J. [Technische Univ. Muenchen, Garching (Germany). Physik-Department; Ring, P. [Technische Univ. Muenchen, Garching (Germany). Physik-Department
1996-10-14
The cranked relativistic mean field approach is applied for a systematic investigation of superdeformed rotational bands observed in the A {proportional_to}140-150 mass region. The present investigation covers yrast and in some cases also excited superdeformed bands of all nuclei of this mass region in which such bands have been observed so far. Using the parameter set NL1, which has been adjusted ten years ago to a few spherical nuclei, reasonable agreement with experimental data is obtained throughout the mass region under investigation. It is shown that the calculated properties of superdeformed rotational bands such as the dependence of the dynamic moment of inertia J{sup (2)} with respect to the rotational frequency and the absolute value of the charge quadrupole moment Q{sub 0} depends sensitively on the number of occupied high-N intruder orbitals. This is in agreement both with previous investigations within the cranked Nilsson-Strutinsky and the cranked Woods-Saxon-Strutinsky approaches and with available experimental data. (orig.).
ZhangHongfei; ZuoWei; SoojaeRenIm; ZhouXiaohong; LiJunqing
2003-01-01
In recent years the discovery of Super Heavy Element (SHE) with atomic number Z=108～116 has opened up a new era of research in nuclear physics, however, the extreme difficulties to synthesize SHE greatly restrict the experimental studies on it, so that the theoretical studies are very important. The Relativistic Mean Field theory (RMF) is proved to be a simple and successful theory due to its great success in describing the bulk properties at the β-stable valley, as well as nuclei far from the β-stable line, and gives good predictions for nuclei far beyond the end of the known periodic table. In the framework of RMF we have calculated the properties on SHN such as the binding energy, the deformation, single and double neutron separation energy, and the a-decay half-life and so on for nuclei Z=108～114 and N=156～190. The axial deformations considered by using the expansion of harmonic oscillator basis. The Lagrangian wc have used is as the following form:
Isoscalar Giant Resonances of 120Sn in the Quasiparticle Relativistic Random Phase Approximation
CAO Li-Gang; MA Zhong-Yu
2004-01-01
@@ The quasiparticle relativistic random phase approximation (QRRPA) is formulated based on the relativistic mean field ground state in the response function formalism. The pairing correlations are taken into account in the Bardeen-Cooper-Schrieffer approximation with a constant pairing gap. The numerical calculations are performed in the case of various isoscalar giant resonances of nucleus 120Sn with parameter set NL3. The calculated results show that the QRRPA approach could satisfactorily reproduce the experimental data of the energies of low-lying states.
El Rhazouani, O.; Benyoussef, A.; Naji, S.; El Kenz, A.
2014-03-01
The double perovskite (DP) Sr2CrReO6, with its high Curie temperature, is a good candidate for magneto-electric and magneto-optic applications. Thus, a theoretical study by Monte Carlo Simulation (MCS) and Mean Field Approximation (MFA) in the context of the Ising model is important for a better understanding of the magnetic behavior of this material. The critical behavior of the magnetization and the susceptibility of this system have been determined. The phase diagrams depending on the exchange couplings and the crystal fields have been given. The values of critical exponents are also reported.
A systematic study of even-even nuclei in the nuclear chart by the relativistic mean field theory
Sumiyoshi, K.; Hirata, D.; Tanihata, I.; Sugahara, Y.; Toki, H. [Institute of Physical and Chemical Research, Wako, Saitama (Japan)
1997-03-01
We study systematically the properties of nuclei in the whole mass range up to the drip lines by the relativistic mean field (RMF) theory with deformations as a microscopic framework to provide the data of nuclear structure in the nuclear chart. The RMF theory is a phenomenological many-body framework, in which the self-consistent equations for nucleons and mesons are solved with arbitrary deformation, and has a potential ability to provide all the essential information of nuclear structure such as masses, radii and deformations together with single particle states and wave functions from the effective lagrangian containing nuclear interaction. As a first step toward the whole project, we study the ground state properties of even-even nuclei ranging from Z=8 to Z=120 up to the proton and neutron drip lines in the RMF theory. We adopt the parameter set TMA, which has been determined by the experimental masses and charge radii in a wide mass range, for the effective lagrangian of the RMF theory. We take into account the axially symmetric deformation using the constrained method on the quadrupole moment. We provide the properties of all even-even nuclei with all the possible ground state deformations extracted from the deformation energy curves by the constrained calculations. By studying the calculated ground state properties systematically, we aim to explore the general trend of masses, radii and deformations in the whole region of the nuclear chart. We discuss the agreement with experimental data and the predictions such as magicness and triaxial deformations beyond the experimental frontier. (author)
Bensadiq, A.; Zaari, H.; Benyoussef, A.; El Kenz, A.
2016-09-01
Using the density functional theory, the electronic structure; density of states, band structure and exchange couplings of Tb Ni4 Si compound have been investigated. Magnetic and magnetocaloric properties of this material have been studied using Monte Carlo Simulation (MCS) and Mean Field Approximation (MFA) within a three dimensional Ising model. We calculated the isothermal magnetic entropy change, adiabatic temperature change and relative cooling power (RCP) for different external magnetic field and temperature. The highest obtained isothermal magnetic entropy change is of -14.52 J kg-1 K-1 for a magnetic field of H=4 T. The adiabatic temperature reaches a maximum value equal to 3.7 K and the RCP maximum value is found to be 125.12 J kg-1 for a field magnetic of 14 T.
Biswal, S K
2014-01-01
We study the isoscalar giant monopole resonance for drip-lines and super heavy nuclei in the frame work of a relativistic mean field theory with scaling approach. The well known extended Thomas-Fermi approximation in the non-linear $\\sigma$-$\\omega$ model is used to estimate the giant monopole excitation energy for some selected light spherical nuclei starting from the region of proton to neutron drip-lines. The application is extended to super heavy region for Z=114 and 120, which are predicted by several models as the next proton magic number beyond Z=82. We compared the excitation energy obtained by four successful force parameters NL1, NL3, NL3$^*$ and FSUGold. The monopole energy decreases toward the proton and neutron drip-lines in an isotopic chain for lighter mass nuclei contrary to a monotonous decrease for super heavy isotopes. The maximum and minimum monopole excitation energies are obtained for nuclei with minimum and maximum isospin, respectively in an isotopic chain.
Bhuyan, M.; Gupta, S. K. Patra Raj K.
2010-01-01
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 Z=117 element, strarting 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 prolate to a oblate shape structures of Z=11...
The phase transition in hot $\\Lambda$ hypernuclei within relativistic Thomas-Fermi approximation
Hu, Jinniu; Bao, Shishao; Shen, Hong
2016-01-01
A self-consistent description for hot $\\Lambda$ hypernuclei in hypothetical big boxes is developed within the relativistic Thomas-Fermi approximation in order to investigate directly the liquid-gas phase coexistence in strangeness finite nuclear systems. We use the relativistic mean-field model for nuclear interactions. The temperature dependence of $\\Lambda$ hyperon density, $\\Lambda$ hyperon radius, excitation energies, specific heat, and the binding energies of $\\Lambda$ hypernuclei from $^{16}_{\\Lambda}$O to $^{208}_{\\Lambda}$Pb in phase transition region are calculated by using the subtraction procedure in order to separate the hypernucleus from the surrounding baryon gas. The $\\Lambda$ central density is very sensitive to the temperature. The radii of $\\Lambda$ hyperon at high temperature become very large. In the relativistic Thomas-Fermi approximation with the subtraction procedure, the properties of hypernuclei are independent of the size of the box in which the calculation is performed. The level de...
Pawlak, A., E-mail: pawlak@amu.edu.pl [Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61–614 Poznań (Poland); Gülpınar, G. [Department of Physics, Dokuz Eylül University, 35160 İzmir (Turkey); Erdem, R. [Department of Physics, Akdeniz University, 07058 Antalya (Turkey); Ağartıoğlu, M. [Institute of Science, Dokuz Eylül University, 35160 İzmir (Turkey)
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. - Highlights: • MFA calculation of the quadrupolar and dipolar susceptibility in BEG model is given • The crystal-field variation of susceptibilities near the multi-critical points is examined • There are broad peaks in the quadrupolar susceptibility in the vicinity of CP • These maxima are remembrances of the very strong quadrupolar Fluctuations.
Niu, YiFei; Vretenar, Dario; Meng, Jie
2011-01-01
We introduce a self-consistent microscopic theoretical framework for modelling the process of electron capture on nuclei in stellar environment, based on relativistic energy density functionals. The finite-temperature relativistic mean-field model is used to calculate the single-nucleon basis and the occupation factors in a target nucleus, and $J^{\\pi} = 0^{\\pm}$, $1^{\\pm}$, $2^{\\pm}$ charge-exchange transitions are described by the self-consistent finite-temperature relativistic random-phase approximation. Cross sections and rates are calculated for electron capture on 54,56Fe and 76,78Ge in stellar environment, and results compared with predictions of similar and complementary model calculations.
Bhuyan, M
2010-01-01
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 Z=117 element, strarting 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 prolate to a oblate shape structures of Z=117 nucleus in our mean field approach. The most stable isotope (largest binding energy per nucleon) is found to be the $^{288}$117 nucleus. Also, the Q-value of $\\alpha$-decay $Q_\\alpha$ and the half-lives $T_{\\alpha}$ are calculated for the $\\alpha$-decay chains of $^{293}$117 and $^{294}$117, supporting the magic numbers at N=172 and/ or 184.
Pais, Helena
2016-01-01
The Vlasov formalism is extended to relativistic mean-field hadron models with non-linear terms up to fourth order and applied to the calculation of the crust-core transition density. The effect of the nonlinear $\\omega\\rho$ and $\\sigma\\rho$ coupling terms on the crust-core transition density and pressure, and on the macroscopic properties of some families of hadronic stars is investigated. For that purpose, six families of relativistic mean field models are considered. Within each family, the members differ in the symmetry energy behavior. For all the models, the dynamical spinodals are calculated, and the crust-core transition density and pressure, and the neutron star mass-radius relations are obtained. The effect on the star radius of the inclusion of a pasta calculation in the inner crust is discussed. The set of six models that best satisfy terrestrial and observational constraints predicts a radius of 13.6$\\pm$0.3 km and a crust thickness of $1.36\\pm 0.06$km for a 1.4 $M_\\odot$ star.
M MOUSAVI; M R SHOJAEI
2017-02-01
In this work, we have obtained energy levels and charge radius for the $\\beta$-stability line nucleus, in relativistic shell model. In this model, we considered a close shell for each nucleus containing double magicnumber and a single nucleon energy level. Here we have taken $^{41}$Ca with a single neutron in the $^{40}$Ca core as an illustrative example. Then we have selected the Eckart plus Hulthen potentials for interaction between the coreand 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, $^{41}$Ca, $^{49}$Ca and $^{57}$Ni. Our results are in agreement with experimental values and hence this model can be applied for similar nuclei.
Haji Ali, Abdul Lateef
2016-01-08
I discuss using single level and multilevel Monte Carlo methods to compute quantities of interests of a stochastic particle system in the mean-field. In this context, the stochastic particles follow a coupled system of Ito stochastic differential equations (SDEs). Moreover, this stochastic particle system converges to a stochastic mean-field limit as the number of particles tends to infinity. I start by recalling the results of applying different versions of Multilevel Monte Carlo (MLMC) for particle systems, both with respect to time steps and the number of particles and using a partitioning estimator. Next, I expand on these results by proposing the use of our recent Multi-index Monte Carlo method to obtain improved convergence rates.
Separable approximation method for two-body relativistic scattering
Tandy, P.C.; Thaler, R.M.
1988-03-01
A method for defining a separable approximation to a given interaction within a two-body relativistic equation, such as the Bethe-Salpeter equation, is presented. The rank-N separable representation given here permits exact reproduction of the T matrix on the mass shell and half off the mass shell at N selected bound state and/or continuum values of the invariant mass. The method employed is a four-space generalization of the separable representation developed for Schroedinger interactions by Ernst, Shakin, and Thaler, supplemented by procedures for dealing with the relativistic spin structure in the case of Dirac particles.
Separable approximation method for two-body relativistic scattering
Tandy, P. C.; Thaler, R. M.
1988-03-01
A method for defining a separable approximation to a given interaction within a two-body relativistic equation, such as the Bethe-Salpeter equation, is presented. The rank-N separable representation given here permits exact reproduction of the T matrix on the mass shell and half off the mass shell at N selected bound state and/or continuum values of the invariant mass. The method employed is a four-space generalization of the separable representation developed for Schrödinger interactions by Ernst, Shakin, and Thaler, supplemented by procedures for dealing with the relativistic spin structure in the case of Dirac particles.
The Post-Newtonian Approximation for Relativistic Compact Binaries
Futamase Toshifumi
2007-03-01
Full Text Available We discuss various aspects of the post-Newtonian approximation in general relativity. After presenting the foundation based on the Newtonian limit, we show a method to derive post-Newtonian equations of motion for relativistic compact binaries based on a surface integral approach and the strong field point particle limit. As an application we derive third post-Newtonian equations of motion for relativistic compact binaries which respect the Lorentz invariance in the post-Newtonian perturbative sense, admit a conserved energy, and are free from any ambiguity.
Sereda, Yuriy V.; Ortoleva, Peter J.
2014-04-01
A closed kinetic equation for the single-particle density of a viscous simple liquid is derived using a variational method for the Liouville equation and a coarse-grained mean-field (CGMF) ansatz. The CGMF ansatz is based on the notion that during the characteristic time of deformation a given particle interacts with many others so that it experiences an average interaction. A trial function for the N-particle probability density is constructed using a multiscale perturbation method and the CGMF ansatz is applied to it. The multiscale perturbation scheme is based on the ratio of the average nearest-neighbor atom distance to the total size of the assembly. A constraint on the initial condition is discovered which guarantees that the kinetic equation is mass-conserving and closed in the single-particle density. The kinetic equation has much of the character of the Vlasov equation except that true viscous, and not Landau, damping is accounted for. The theory captures condensation kinetics and takes much of the character of the Gross-Pitaevskii equation in the weak-gradient short-range force limit.
Relativistic equation of state at subnuclear densities in the Thomas-Fermi approximation
Zhang, Z W
2014-01-01
We study the non-uniform nuclear matter using the self-consistent Thomas--Fermi approximation with a relativistic mean-field model. The non-uniform matter is assumed to be composed of a lattice of heavy nuclei surrounded by dripped nucleons. At each temperature $T$, proton fraction $Y_p$, and baryon mass density $\\rho_B$, we determine the thermodynamically favored state by minimizing the free energy with respect to the radius of the Wigner--Seitz cell, while the nucleon distribution in the cell can be determined self-consistently in the Thomas--Fermi approximation. A detailed comparison is made between the present results and previous calculations in the Thomas--Fermi approximation with a parameterized nucleon distribution that has been adopted in the widely used Shen EOS.
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.
Lu, Bing-Nan; Zhao, En-Guang; Zhou, Shan-Gui
2013-01-01
We have developed multi-dimensional constrained covariant density functional theories (MDC-CDFT) for finite nuclei in which the shape degrees of freedom \\beta_{\\lambda\\mu} with even \\mu, e.g., \\beta_{20}, \\beta_{22}, \\beta_{30}, \\beta_{32}, \\beta_{40}, etc., can be described simultaneously. The functional can be one of the following four forms: the meson exchange or point-coupling nucleon interactions combined with the non-linear or density-dependent couplings. For the pp channel, either the BCS approach or the Bogoliubov transformation is implemented. The MDC-CDFTs with the BCS approach for the pairing (in the following labelled as MDC-RMF models with RMF standing for "relativistic mean field") have been applied to investigate multi-dimensional potential energy surfaces and the non-axial octupole $Y_{32}$-correlations in N=150 isotones. In this contribution we present briefly the formalism of MDC-RMF models and some results from these models. The potential energy surfaces with and without triaxial deformatio...
Sharma, M M; Münzenberg, G
2004-01-01
We have investigated properties of $\\alpha$-decay chains of recently produced superheavy elements Z=115 and Z=113 using the new Lagrangian model NL-SV1 with inclusion of the vector self-coupling of $\\omega$ meson in the framework of the relativistic mean-field theory. It is shown that the experimentally observed alpha-decay energies and half-lives are reproduced well by this Lagrangian model. Further calculations for the heavier elements with Z=117-125 show that these nuclei are superdeformed with a prolate shape in the ground state. A superdeformed shell-closure at Z=118 lends an additional binding and an extra stability to nuclei in this region. Consequently, it is predicted that the corresponding $Q_\\alpha$ values provide $\\alpha$-decay half-lives for heavier superheavy nuclei within the experimentally feasible conditions. The results are compared with those of macroscopic-microscopic approaches. A perspective of the difference in shell effects amongst various approaches is presented and its consequences o...
Electron correlation within the relativistic no-pair approximation
Almoukhalalati, Adel; Knecht, Stefan; Jensen, Hans Jørgen Aa.; Dyall, Kenneth G.; Saue, Trond
2016-08-01
This paper addresses the definition of correlation energy within 4-component relativistic atomic and molecular calculations. In the nonrelativistic domain the correlation energy is defined as the difference between the exact eigenvalue of the electronic Hamiltonian and the Hartree-Fock energy. In practice, what is reported is the basis set correlation energy, where the "exact" value is provided by a full Configuration Interaction (CI) calculation with some specified one-particle basis. The extension of this definition to the relativistic domain is not straightforward since the corresponding electronic Hamiltonian, the Dirac-Coulomb Hamiltonian, has no bound solutions. Present-day relativistic calculations are carried out within the no-pair approximation, where the Dirac-Coulomb Hamiltonian is embedded by projectors eliminating the troublesome negative-energy solutions. Hartree-Fock calculations are carried out with the implicit use of such projectors and only positive-energy orbitals are retained at the correlated level, meaning that the Hartree-Fock projectors are frozen at the correlated level. We argue that the projection operators should be optimized also at the correlated level and that this is possible by full Multiconfigurational Self-Consistent Field (MCSCF) calculations, that is, MCSCF calculations using a no-pair full CI expansion, but including orbital relaxation from the negative-energy orbitals. We show by variational perturbation theory that the MCSCF correlation energy is a pure MP2-like correlation expression, whereas the corresponding CI correlation energy contains an additional relaxation term. We explore numerically our theoretical analysis by carrying out variational and perturbative calculations on the two-electron rare gas atoms with specially tailored basis sets. In particular, we show that the correlation energy obtained by the suggested MCSCF procedure is smaller than the no-pair full CI correlation energy, in accordance with the underlying
Roussou, A.; Smyrnakis, J.; Magiropoulos, M.; Efremidis, Nikolaos K.; Kavoulakis, G. M.
2017-03-01
Motivated by recent experiments on Bose-Einstein condensed atoms which rotate in annular and/or toroidal traps, we study the effect of the finiteness of the atom number N on the states of lowest energy for a fixed expectation value of the angular momentum, under periodic boundary conditions. To attack this problem, we develop a general strategy, considering a linear superposition of the eigenstates of the many-body Hamiltonian, with amplitudes that we extract from the mean-field approximation. This many-body state breaks the symmetry of the Hamiltonian; it has the same energy to leading order in N as the mean-field state and the corresponding eigenstate of the Hamiltonian, however, it has a lower energy to subleading order in N and thus it is energetically favorable.
Extended quasiparticle approximation for relativistic electrons in plasmas
V.G.Morozov
2006-01-01
Full Text Available Starting with Dyson equations for the path-ordered Green's function, it is shown that the correlation functions for relativistic electrons (positrons in a weakly coupled non-equilibrium plasmas can be decomposed into sharply peaked quasiparticle parts and off-shell parts in a rather general form. To leading order in the electromagnetic coupling constant, this decomposition yields the extended quasiparticle approximation for the correlation functions, which can be used for the first principle calculation of the radiation scattering rates in QED plasmas.
Relativistic quasiparticle random phase approximation in deformed nuclei
Pena Arteaga, D.
2007-06-25
Covariant density functional theory is used to study the influence of electromagnetic radiation on deformed superfluid nuclei. The relativistic Hartree-Bogolyubov equations and the resulting diagonalization problem of the quasiparticle random phase approximation are solved for axially symmetric systems in a fully self-consistent way by a newly developed parallel code. Three different kinds of high precision energy functionals are investigated and special care is taken for the decoupling of the Goldstone modes. This allows the microscopic investigation of Pygmy and scissor resonances in electric and magnetic dipole fields. Excellent agreement with recent experiments is found and new types of modes are predicted for deformed systems with large neutron excess. (orig.)
Approximate Relativistic Solutions for One-Dimensional Cylindrical Coaxial Diode
曾正中; 刘国治; 邵浩
2002-01-01
Two approximate analytical relativistic solutions for one-dimensional, space-chargelimited cylindrical coaxial diode are derived and utilized to compose best-fitting approximate solutions. Comparison of the best-fitting solutions with the numerical one demonstrates an error of about 11% for cathode-inside arrangement and 12% in the cathode-outside case for ratios of larger to smaller electrode radius from 1.2 to 10 and a voltage above 0.5 MV up to 5 MV. With these solutions the diode lengths for critical self-magnetic bending and for the condition under which the parapotential model validates are calculated to be longer than 1 cm up to more than 100 cm depending on voltage, radial dimensions and electrode arrangement. The influence of ion flow from the anode on the relativistic electron-only solution is numerically computed, indicating an enhancement factor of total diode current of 1.85 to 4.19 related to voltage, radial dimension and electrode arrangement.
Relativistic Quasiparticle Random Phase Approximation with a Separable Pairing Force
TIAN Yuan; MA Zhong-Yu; Ring Peter
2009-01-01
In our previous work [Phys. Lett. (to be published), Chin. Phys. Lett. 23 (2006) 3226], we introduced a separable pairing force for relativistic Hartree-Bogoliubov calculations. This force was adjusted to reproduce the pairing properties of the Gogny force in nuclear matter. By using the well known techniques of Talmi and Moshinsky it can be expanded in a series of separable terms and converges quickly after a few terms. It was found that the pairing properties can be depicted on almost the same footing as the original pairing interaction, not only in nuclear matter, but also in finite nuclei. In this study, we construct a relativistic quasiparticle random phase approximation (RQRPA ) with this separable pairing interaction and calculate the excitation energies of the first excited 2+ .states and reduced B(E2; 0+ → 2+) transition rates for a chain of Sn isotopes in RQRPA. Compared with the results of the full Gogny force, we find that this simple separable pairing interaction can describe the pairing properties of the excited vibrational states as well as the original pairing interaction.
A simple approximation for the current-voltage characteristics of high-power, relativistic diodes
Ekdahl, Carl
2016-06-01
A simple approximation for the current-voltage characteristics of a relativistic electron diode is presented. The approximation is accurate from non-relativistic through relativistic electron energies. Although it is empirically developed, it has many of the fundamental properties of the exact diode solutions. The approximation is simple enough to be remembered and worked on almost any pocket calculator, so it has proven to be quite useful on the laboratory floor.
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.
Satoh, Akira; Sakuda, Yasuhiro
2007-04-15
We have considered a semi-dense dispersion composed of ferromagnetic rodlike particles with a magnetic moment normal to the particle axis to investigate the rheological properties and particle orientational distribution in a simple shear flow as well as an external magnetic field. We have adopted the mean field approximation to take into account magnetic particle-particle interactions. The basic equation of the orientational distribution function has been derived from the balance of the torques and solved numerically. The results obtained here are summarized as follows. For a very strong magnetic field, the magnetic moment of the rodlike particle is strongly restricted in the field direction, so that the particle points to directions normal to the flow direction (and also to the magnetic field direction). This characteristic of the particle orientational distribution is also valid for the case of a strong particle-particle interaction, as in the strong magnetic field case. To the contrary, for a weak interaction among particles, the particle orientational distribution is governed by a shear flow as well as an applied magnetic field. When the magnetic particle-particle interaction is strong under circumstances of an applied magnetic field, the magnetic moment has a tendency to incline to the magnetic field direction more strongly. This leads to the characteristic that the viscosity decreases with decreasing the distance between particles, and this tendency becomes more significant for a stronger particle-particle interaction. These characteristics concerning the viscosity are quite different from those for a semi-dense dispersion composed of rodlike particles with a magnetic moment along the particle direction.
Mean-field models and exotic nuclei
Bender, M.; Buervenich, T.; Maruhn, J.A.; Greiner, W. [Inst. fuer Theoretische Physik, Univ. Frankfurt (Germany); Rutz, K. [Inst. fuer Theoretische Physik, Univ. Frankfurt (Germany)]|[Gesellschaft fuer Schwerionenforschung mbH, Darmstadt (Germany); Reinhard, P.G. [Inst. fuer Theoretische Physik, Univ. Erlangen (Germany)
1998-06-01
We discuss two widely used nuclear mean-field models, the relativistic mean-field model and the (nonrelativistic) Skyrme-Hartree-Fock model, and their capability to describe exotic nuclei. Test cases are superheavy nuclei and neutron-rich Sn isotopes. New information in this regime helps to fix hitherto loosely determined aspects of the models. (orig.)
Electron correlation within the relativistic no-pair approximation
Almoukhalalati, Adel; Knecht, Stefan; Jensen, Hans Jørgen Aa
2016-01-01
This paper addresses the definition of correlation energy within 4-component relativistic atomic and molecular calculations. In the nonrelativistic domain the correlation energy is defined as the difference between the exact eigenvalue of the electronic Hamiltonian and the Hartree-Fock energy....... In practice, what is reported is the basis set correlation energy, where the "exact" value is provided by a full Configuration Interaction (CI) calculation with some specified one-particle basis. The extension of this definition to the relativistic domain is not straightforward since the corresponding......-like correlation expression, whereas the corresponding CI correlation energy contains an additional relaxation term. We explore numerically our theoretical analysis by carrying out variational and perturbative calculations on the two-electron rare gas atoms with specially tailored basis sets...
Normal modes of relativistic systems in post Newtonian approximation
Sobouti, Y
1998-01-01
We use the post Newtonian (pn) order of Liouville's equation (pnl) to study the normal modes of oscillation of a relativistic system. In addition to classical modes, we are able to isolate a new class of oscillations that arise from perturbations of the space-time metric. In the first pn order; a) their frequency is an order q smaller than the classical frequencies, where q is a pn expansion parameter; b) they are not damped, for there is no gravitational wave radiation in this order; c) they are not coupled with the classical modes in q order; d) in a spherically symmetric system, they are designated by a pair of angular momentum eigennumbers, (j,m), of a pair of phase space angular momentum operators (J^2,J_z). Hydrodynamical behavior of these new modes is also investigated; a) they do not disturb the equilibrium of the classical fluid; b) they generate macroscopic toroidal motions that in classical case would be neutral; c) they give rise to an oscillatory g_{0i} component of the metric tensor that otherwi...
Gomes, Diogo A.
2014-01-06
In this talk we will report on new results concerning the existence of smooth solutions for time dependent mean-field games. This new result is established through a combination of various tools including several a-priori estimates for time-dependent mean-field games combined with new techniques for the regularity of Hamilton-Jacobi equations.
Nonrelativistic mean-field description of the deformation of Λ hypernuclei
无
2009-01-01
The deformations of light Λ hypernuclei are studied in an extended nonrelativistic deformed Skyrme-Hartree-Fock approach with realistic modern nucleonic Skyrme forces,pairing correlations,and a microscopical lambda-nucleon interaction derived from Brueckner-Hartree-Fock calculations.Compared to the large effect of an additional Λ particle on nuclear deformation in the light soft nuclei within relativistic mean field method,this effect is much smaller in the nonrelativistic mean-field approximation.
Bernardos, P. [Universidad de Cantabria, Departamento de Matematica Aplicada y Ciencias de la Computacion, 39005, Santander (Spain); Fomenko, V.N. [St Petersburg University for Railway Engineering, Department of Mathematics, 190031, St Petersburg (Russian Federation); Marcos, S.; Niembro, R. [Universidad de Cantabria, Departamento de Fisica Moderna, 39005, Santander (Spain); Lopez-Quelle, M. [Universidad de Cantabria, Departamento de Fisica Aplicada, 39005, Santander (Spain); Savushkin, L.N. [St Petersburg University for Telecommunications, Department of Physics, 191186, St Petersburg (Russian Federation)
2001-02-01
An effective nuclear model describing {omega}-, {rho}- and axial-mesons as gauge fields is applied to nuclear matter in the relativistic Hartree-Fock approximation. The isoscalar two-pion exchange is simulated by a scalar field s similar to that used in the conventional relativistic mean-field approach. Two more scalar fields are essential ingredients of the present treatment: the {sigma}-field, the chiral partner of the pion, and the {sigma}-field, the Higgs field for the {omega}-meson. Two versions of the model are used depending on whether the {sigma}-field is considered as a dynamical variable or 'frozen', by taking its mass as infinite. The model contains four free parameters in the first case and three in the second one which are fitted to the nuclear matter saturation conditions. The nucleon and meson effective masses, compressibility modulus and symmetry energy are calculated. The results prove the reliability of the Dirac-Hartree-Fock approach within the linear realization of the chiral symmetry. (author)
Petersen, Kaare Brandt
2006-01-01
This thesis describes investigations and improvements of a technique for Independent Component Analysis (ICA), called "Mean Field ICA". The main focus of the thesis is the optimization part of the algorithm, the so-called "EM algorithm". Using different approaches it is demonstrated that the EM...... Gradient Recipe is applicable to a wide selection of models. Furthermore, the Mean Field ICA model is extended to incorporate ltering over time in a so-called "convolutive ICA" model. Finally, by using mixture of Gaussians as source priors, the generative and ltering approach to ICA is compared...
An introduction to relativistic magnetohydrodynamics I. The force-free approximation
Karas, Vladimír
2005-12-01
This lecture summarizes basic equations of relativistic magnetohydrodynamics (MHD). The aim of the lecture is to present important relations and approximations that have been often employed and found useful in the astrophysical context, namely, in situations when plasma motion is governed by magnetohydrodynamic and gravitational effects competing with each other near a black hole.
Guerra, E.M. de [Inst. de Estructura de la Materia, Consejo Superior de Investigaciones Cientificas (Spain)
2001-07-01
In these talks, we review non relativistic selfconsistent mean field theories, their scope and limitations. We first discuss static and time dependent mean field approaches for particles and quasiparticles, together with applications. We then discuss extensions that go beyond the non-relativistic independent particle limit. On the one hand, we consider extensions concerned with restoration of symmetries and with the treatment of collective modes, particularly by means of quantized ATDHF. On the other hand, we consider extensions concerned with the relativistic dynamics of bound nucleons. We present data on nucleon momentum distributions that show the need for relativistic mean field approach and probe the limits of the mean field concept. Illustrative applications of various methods are presented stressing the role that selfconsistency plays in providing a unifying reliable framework to study all sorts of properties and phenomena. From global properties such as size, mass, lifetime,.., to detailed structure in excitation spectra (high spin, RPA modes,..), as well as charge, magnetization and velocity distributions. (orig.)
Nonasymptotic mean-field games
Tembine, Hamidou
2014-12-01
Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists to approximate large games by a stylized game model with a continuum of players. The approach has been shown to be useful in some applications. However, the stylized game model with continuum of decision-makers is rarely observed in practice and the approximation proposed in the asymptotic regime is meaningless for networked systems with few entities. In this paper we propose a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through a dynamic auction with asymmetric valuation distributions.
Nonasymptotic mean-field games
Tembine, Hamidou
2014-12-01
Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists of approximating large games by a stylized game model with a continuum of players. The approach has been shown to be useful in some applications. However, the stylized game model with continuum of decision-makers is rarely observed in practice and the approximation proposed in the asymptotic regime is meaningless for networks with few entities. In this paper, we propose a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through various examples including dynamic auction with asymmetric valuation distributions, and spiteful bidders.
Vollhardt, D.; Byczuk, K.; Kollar, M.
2011-01-01
The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the ...
Egorova, Irina A
2016-01-01
New results for electric dipole strength in the chain of even-even Calcium isotopes with the mass numbers A = 40 - 54 are presented. Starting from the covariant Lagrangian of Quantum Hadrodynamics, spectra of collective vibrations (phonons) and phonon-nucleon coupling vertices for $J \\leq 6$ and normal parity were computed in a self-consistent relativistic quasiparticle random phase approximation (RQRPA). These vibrations coupled to Bogoliubov two-quasiparticle configurations (2q$\\otimes$phonon) form the model space for the calculations of the dipole response function in the relativistic quasiparticle time blocking approximation (RQTBA). The results for giant dipole resonance in the latter approach are compared to those obtained in RQRPA and to available data. Evolution of the dipole strength with neutron number is investigated for both high-frequency giant dipole resonance (GDR) and low-lying strength. Development of a pygmy resonant structure on the low-energy shoulder of GDR is traced and analyzed in terms...
Filatov, Michael; Cremer, Dieter
2004-06-22
A new method for calculating the indirect nuclear spin-spin coupling constant within the regular approximation to the exact relativistic Hamiltonian is presented. The method is completely analytic in the sense that it does not employ numeric integration for the evaluation of relativistic corrections to the molecular Hamiltonian. It can be applied at the level of conventional wave function theory or density functional theory. In the latter case, both pure and hybrid density functionals can be used for the calculation of the quasirelativistic spin-spin coupling constants. The new method is used in connection with the infinite-order regular approximation with modified metric (IORAmm) to calculate the spin-spin coupling constants for molecules containing heavy elements. The importance of including exact exchange into the density functional calculations is demonstrated.
Mean field theory for fermion-based U(2) anyons
McGraw, P
1996-01-01
The energy density is computed for a U(2) Chern-Simons theory coupled to a non-relativistic fermion field (a theory of ``non-Abelian anyons'') under the assumptions of uniform charge and matter density. When the matter field is a spinless fermion, we find that this energy is independent of the two Chern-Simons coupling constants and is minimized when the non-Abelian charge density is zero. This suggests that there is no spontaneous breaking of the SU(2) subgroup of the symmetry, at least in this mean-field approximation. For spin-1/2 fermions, we find self-consistent mean-field states with a small non-Abelian charge density, which vanishes as the theory of free fermions is approached.
Continuous time finite state mean field games
Gomes, Diogo A.
2013-04-23
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games. © 2013 Springer Science+Business Media New York.
PADÉ APPROXIMANTS FOR THE EQUATION OF STATE FOR RELATIVISTIC HYDRODYNAMICS BY KINETIC THEORY
Tsai, Shang-Hsi; Yang, Jaw-Yen, E-mail: shanghsi@gmail.com [Institute of Applied Mechanics, National Taiwan University, Taipei 10764, Taiwan (China)
2015-07-20
A two-point Padé approximant (TPPA) algorithm is developed for the equation of state (EOS) for relativistic hydrodynamic systems, which are described by the classical Maxwell–Boltzmann statistics and the semiclassical Fermi–Dirac statistics with complete degeneracy. The underlying rational function is determined by the ratios of the macroscopic state variables with various orders of accuracy taken at the extreme relativistic limits. The nonunique TPPAs are validated by Taub's inequality for the consistency of the kinetic theory and the special theory of relativity. The proposed TPPA is utilized in deriving the EOS of the dilute gas and in calculating the specific heat capacity, the adiabatic index function, and the isentropic sound speed of the ideal gas. Some general guidelines are provided for the application of an arbitrary accuracy requirement. The superiority of the proposed TPPA is manifested in manipulating the constituent polynomials of the approximants, which avoids the arithmetic complexity of struggling with the modified Bessel functions and the hyperbolic trigonometric functions arising from the relativistic kinetic theory.
González-Jiménez, R; Donnelly, T W
2015-01-01
We study parity violation in quasielastic (QE) electron-nucleus scattering using the relativistic impulse approximation. Different fully relativistic approaches have been considered to estimate the effects associated with the final-state interactions. We have computed the parity-violating quasielastic (PVQE) asymmetry and have analyzed its sensitivity to the different ingredients that enter in the description of the reaction mechanism: final-state interactions, nucleon off-shellness effects, current gauge ambiguities. Particular attention has been paid to the description of the weak neutral current form factors. The PVQE asymmetry is proven to be an excellent observable when the goal is to get precise information on the axial-vector sector of the weak neutral current. Specifically, from measurements of the asymmetry at backward scattering angles good knowledge of the radiative corrections entering in the isovector axial-vector sector can be gained. Finally, scaling properties shown by the interference $\\gamma...
{beta}-decay rates of r-process nuclei in the relativistic quasiparticle random phase approximation
Niksic, T.; Marketin, T.; Vretenar, D. [Zagreb Univ. (Croatia). Faculty of Science, Physics Dept.; Paar, N. [Technische Univ. Darmstadt (Germany). Inst. fuer Kernphysik; Ring, P. [Technische Univ. Muenchen, Garching (Germany). Physik-Department
2004-12-08
The fully consistent relativistic proton-neutron quasiparticle random phase approximation (PN-RQRPA) is employed in the calculation of {beta}-decay half-lives of neutron-rich nuclei in the N{approx}50 and N{approx}82 regions. A new density-dependent effective interaction, with an enhanced value of the nucleon effective mass, is used in relativistic Hartree-Bogolyubov calculation of nuclear ground states and in the particle-hole channel of the PN-RQRPA. The finite range Gogny D1S interaction is employed in the T=1 pairing channel, and the model also includes a proton-neutron particle-particle interaction. The theoretical half-lives reproduce the experimental data for the Fe, Zn, Cd, and Te isotopic chains, but overestimate the lifetimes of Ni isotopes and predict a stable {sup 132}Sn. (orig.)
Relativistic gravitational collapse in comoving coordinates: The post-quasistatic approximation
Herrera, L
2010-01-01
A general iterative method proposed some years ago for the description of relativistic collapse, is presented here in comoving coordinates. For doing that we redefine the basic concepts required for the implementation of the method for comoving coordinates. In particular the definition of the post-quasistatic approximation in comoving coordinates is given. We write the field equations, the boundary conditions and a set of ordinary differential equations (the surface equations) which play a fundamental role in the algorithm. As an illustration of the method, we show how to build up a model inspired in the well known Schwarzschild interior solution. Both, the adiabatic and non adiabatic, cases are considered.
Yang, Ding; Ma, Zhongyu
2013-01-01
Journal of Combinatorial Theory, Series B, 98(1):173-225, 2008n exotic nuclei are studied in the framework of a fully self-consistent relativistic continuum random phase approximation (RCRPA). In this method the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single particle Green's function. Different from the cases in stable nuclei, there are strong low-energy excitations in neutron-rich nuclei and proton-rich nuclei. The neutron or proton excess pushes the centroid of the strength function to lower energies and increases the fragmentation of the strength distribution. The effect of treating the contribution of continuum exactly are also discussed.
Chen Wen-Li; Wei Gao-Feng
2011-01-01
By applying a Pekeris-type approximation to the centrifugal term, we study the spin symmetry of a Dirac nucleon subjected to scalar and vector modified Rosen-Morse potentials. A complicated energy equation and associated twocomponent spinors with arbitrary spin-orbit coupling quantum number k are presented. The positive-energy bound states are checked numerically in the case of spin symmetry. The relativistic modified Rosen-Morse potential cannot trap a Dirac nucleon in the limiting case α→ 0.
Satoh, Akira
2005-09-01
We have theoretically investigated the particle orientational distribution and viscosity of a dense colloidal dispersion composed of ferromagnetic spherocylinder particles under an applied magnetic field. The mean field approximation has been applied to take into account the magnetic interactions of the particle of interest with the other ones that belong to the neighboring clusters, besides those that belong to its own cluster. The basic equation of the orientational distribution function, which is an integrodifferential equation, has approximately been solved by Galerkin's method and the method of successive approximation. Some of the main results obtained here are summarized as follows. Even when the magnetic interaction between particles is of the order of the thermal energy, the effect of particle-particle interactions on the orientational distribution comes to appear more significant with increasing volumetric fraction of particles; the orientational distribution function exhibits a sharper peak in the direction nearer to the magnetic field one as the volumetric fraction increases. Such a significant inclination of the particle in the field direction induces the large increase in viscosity in the range of larger values of the volumetric fraction. The above-mentioned characteristics of the orientational distribution and viscosity come to appear more significantly when the influence of the applied magnetic field is not so strong compared with that of magnetic particle-particle interactions.
Geroyannis, Vassilis S
2014-01-01
We develop a "hybrid approximative scheme" in the framework of the post-Newtonian approximation for computing general-relativistic polytropic models simulating neutron stars in critical rigid rotation. We treat the differential equations governing such a model as a "complex initial value problem", and we solve it by using the so-called "complex-plane strategy". We incorporate into the computations the complete solution for the relativistic effects, this issue representing a significant improvement with regard to the classical post-Newtonian approximation, as verified by extended comparisons of the numerical results.
General Relativistic Radiant Shock Waves in the Post-Quasistatic Approximation
H, Jorge A Rueda [Centro de Fisica Fundamental, Universidad de Los Andes, Merida 5101, Venezuela Escuela de Fisica, Universidad Industrial de Santander, A.A. 678, Bucaramanga (Colombia); Nunez, L A [Centro de Fisica Fundamental, Universidad de Los Andes, Merida 5101, Venezuela Centro Nacional de Calculo Cientifico, Universidad de Los Andes, CeCalCULA, Corporacion Parque Tecnologico de Merida, Merida 5101, Venezuela (Venezuela)
2007-05-15
An evolution of radiant shock wave front is considered in the framework of a recently presented method to study self-gravitating relativistic spheres, whose rationale becomes intelligible and finds full justification within the context of a suitable definition of the post-quasistatic approximation. The spherical matter configuration is divided into two regions by the shock and each side of the interface having a different equation of state and anisotropic phase. In order to simulate dissipation effects due to the transfer of photons and/or neutrinos within the matter configuration, we introduce the flux factor, the variable Eddington factor and a closure relation between them. As we expected the strong of the shock increases the speed of the fluid to relativistic ones and for some critical values is larger than light speed. In addition, we find that energy conditions are very sensible to the anisotropy, specially the strong energy condition. As a special feature of the model, we find that the contribution of the matter and radiation to the radial pressure are the same order of magnitude as in the mant as in the core, moreover, in the core radiation pressure is larger than matter pressure.
Roles of Antinucleon Degrees of Freedom in the Relativistic Random Phase Approximation
Kurasawa, Haruki
2015-01-01
Roles of antinucleon degrees of freedom in the relativistic random phase approximation(RPA) are investigated. The energy-weighted sum of the RPA transition strengths is expressed in terms of the double commutator between the excitation operator and the Hamiltonian, as in nonrelativistic models. The commutator, however, should not be calculated with a usual way in the local field theory, because, otherwise, the sum vanishes. The sum value obtained correctly from the commutator is infinite, owing to the Dirac sea. Most of the previous calculations takes into account only a part of the nucleon-antinucleon states, in order to avoid the divergence problems. As a result, RPA states with negative excitation energy appear, which make the sum value vanish. Moreover, disregarding the divergence changes the sign of nuclear interactions in the RPA equation which describes the coupling of the nucleon particle-hole states with the nucleon-antinucleon states. Indeed, excitation energies of the spurious state and giant monop...
Complete equation of state for neutron stars using the relativistic Hartree-Fock approximation
Miyatsu, Tsuyoshi; Cheoun, Myung-Ki [Department of Physics, Soongsil University, Seoul 156-743 (Korea, Republic of); Yamamuro, Sachiko; Nakazato, Ken' ichiro [Department of Physics, Faculty of Science and Technology, Tokyo University of Science (TUS), Noda 278-8510 (Japan)
2014-05-02
We construct the equation of state in a wide-density range for neutron stars within relativistic Hartree-Fock approximation. The properties of uniform and nonuniform nuclear matter are studied consistently. The tensor couplings of vector mesons to baryons due to exchange contributions (Fock terms) are included, and the change of baryon internal structure in matter is also taken into account using the quark-meson coupling model. The Thomas-Fermi calculation is adopted to describe nonuniform matter, where the lattice of nuclei and the neutron drip out of nuclei are considered. Even if hyperons exist in the core of a neutron star, we obtain the maximum neutron-star mass of 1.95M{sub ⊙}, which is consistent with the recently observed massive pulsar, PSR J1614-2230. In addition, the strange vector (φ) meson also plays a important role in supporting a massive neutron star.
Relativistic Three-Quark Bound States in Separable Two-Quark Approximation
Öttel, M; Alkofer, R
2002-01-01
Baryons as relativistic bound states in 3-quark correlations are described by an effective Bethe-Salpeter equation when irreducible 3-quark interactions are neglected and separable 2-quark correlations are assumed. We present an efficient numerical method to calculate the nucleon mass and its covariant wave function in this quantum field theoretic quark-diquark model with quark-exchange interaction. Expanding the components of the spinorial wave function in terms of Chebyshev polynomials, the four-dimensional integral equations are in a first step reduced to a coupled set of one-dimensional ones. This set of linear and homogeneous equations defines a generalised eigenvalue problem. Representing the eigenvector corresponding to the largest eigenvalue, the Chebyshev moments are then obtained by iteration. The nucleon mass is implicitly determined by the eigenvalue, and its covariant wave function is reconstructed from the moments within the Chebyshev approximation.
Buchert, Thomas
2012-01-01
In this first paper we present a Lagrangian framework for the description of structure formation in general relativity, restricting attention to irrotational dust matter. As an application we present a self-contained derivation of a general-relativistic analogue of Zel'dovich's approximation for the description of structure formation in cosmology, and compare it with previous suggestions in the literature. This approximation is then investigated: paraphrasing the derivation in the Newtonian framework we provide general-relativistic analogues of the basic system of equations for a single dynamical field variable and recall the first-order perturbation solution of these equations. We then define a general-relativistic analogue of Zel'dovich's approximation and investigate consequences by functionally evaluating relevant variables. We so obtain a possibly powerful model that, although constructed through extrapolation of a perturbative solution, can be used to address non-perturbatively, e.g. problems of structu...
Approximate Harten-Lax-van Leer Riemann solvers for relativistic magnetohydrodynamics
Mignone, Andrea; Bodo, G.; Ugliano, M.
2012-11-01
We review a particular class of approximate Riemann solvers in the context of the equations of ideal relativistic magnetohydrodynamics. Commonly prefixed as Harten-Lax-van Leer (HLL), this family of solvers approaches the solution of the Riemann problem by providing suitable guesses to the outermots characteristic speeds, without any prior knowledge of the solution. By requiring consistency with the integral form of the conservation law, a simplified set of jump conditions with a reduced number of characteristic waves may be obtained. The degree of approximation crucially depends on the wave pattern used in prepresnting the Riemann fan arising from the initial discontinuity breakup. In the original HLL scheme, the solution is approximated by collapsing the full characteristic structure into a single average state enclosed by two outermost fast mangnetosonic speeds. On the other hand, HLLC and HLLD improves the accuracy of the solution by restoring the tangential and Alfvén modes therefore leading to a representation of the Riemann fan in terms of 3 and 5 waves, respectively.
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
Weakly coupled mean-field game systems
Gomes, Diogo A.
2016-07-14
Here, we prove the existence of solutions to first-order mean-field games (MFGs) arising in optimal switching. First, we use the penalization method to construct approximate solutions. Then, we prove uniform estimates for the penalized problem. Finally, by a limiting procedure, we obtain solutions to the MFG problem. © 2016 Elsevier Ltd
A regularized stationary mean-field game
Yang, Xianjin
2016-04-19
In the thesis, we discuss the existence and numerical approximations of solutions of a regularized mean-field game with a low-order regularization. In the first part, we prove a priori estimates and use the continuation method to obtain the existence of a solution with a positive density. Finally, we introduce the monotone flow method and solve the system numerically.
A mean field approach to watershed hydrology
Bartlett, Mark; Porporato, Amilcare
2016-04-01
Mean field theory (also known as self-consistent field theory) is commonly used in statistical physics when modeling the space-time behavior of complex systems. The mean field theory approximates a complex multi-component system by considering a lumped (or average) effect for all individual components acting on a single component. Thus, the many body problem is reduced to a one body problem. For watershed hydrology, a mean field theory reduces the numerous point component effects to more tractable watershed averages, resulting in a consistent method for linking the average watershed fluxes to the local fluxes at each point. We apply this approach to the spatial distribution of soil moisture, and as a result, the numerous local interactions related to lateral fluxes of soil water are parameterized in terms of the average soil moisture. The mean field approach provides a basis for unifying and extending common event-based models (e.g. Soil Conservation Service curve number (SCS-CN) method) with more modern semi-distributed models (e.g. Variable Infiltration Capacity (VIC) model, the Probability Distributed (PDM) model, and TOPMODEL). We obtain simple equations for the fractions of the different source areas of runoff, the spatial variability of runoff, and the average runoff value (i.e., the so-called runoff curve). The resulting space time distribution of soil moisture offers a concise description of the variability of watershed fluxes.
Dimmelmeier, H; Font, J A; Dimmelmeier, Harald; Stergioulas, Nikolaos; Font, Jose A.
2005-01-01
We study non-linear axisymmetric pulsations of rotating relativistic stars using a general relativistic hydrodynamics code under the assumption of a conformal flatness. We compare our results to previous simulations where the spacetime dynamics was neglected. The pulsations are studied along various sequences of both uniformly and differentially rotating relativistic polytropes with index N = 1. We identify several modes, including the lowest-order l = 0, 2, and 4 axisymmetric modes, as well as several axisymmetric inertial modes. Differential rotation significantly lowers mode frequencies, increasing prospects for detection by current gravitational wave interferometers. We observe an extended avoided crossing between the l = 0 and l = 4 first overtones, which is important for correctly identifying mode frequencies in case of detection. For uniformly rotating stars near the mass-shedding limit, we confirm the existence of the mass-shedding-induced damping of pulsations, though the effect is not as strong as i...
Bauso, Dario
2014-01-06
The myth of marriage has been and is still a fascinating historical societal phenomenon. Paradoxically, the empirical divorce rates are at an all-time high. This work describes a unique paradigm for preserving relationships and marital stability from mean-field game theory. We show that optimizing the long-term well-being via effort and society feeling state distribution will help in stabilizing relationships.
Quantum correlations in nuclear mean field theory through source terms
Lee, S J
1996-01-01
Starting from full quantum field theory, various mean field approaches are derived systematically. With a full consideration of external source dependence, the stationary phase approximation of an action gives a nuclear mean field theory which includes quantum correlation effects (such as particle-hole or ladder diagram) in a simpler way than the Brueckner-Hartree-Fock approach. Implementing further approximation, the result can be reduced to Hartree-Fock or Hartree approximation. The role of the source dependence in a mean field theory is examined.
Mean-field Ensemble Kalman Filter
Law, Kody
2015-01-07
A proof of convergence of the standard EnKF generalized to non-Gaussian state space models is provided. A density-based deterministic approximation of the mean-field limiting EnKF (MFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for d < 2 . The fidelity of approximation of the true distribution is also established using an extension of total variation metric to random measures. This is limited by a Gaussian bias term arising from non-linearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
Relativistic RPA in axial symmetry
Arteaga, D Pena; 10.1103/PhysRevC.77.034317
2009-01-01
Covariant density functional theory, in the framework of self-consistent Relativistic Mean Field (RMF) and Relativistic Random Phase approximation (RPA), is for the first time applied to axially deformed nuclei. The fully self-consistent RMF+RRPA equations are posed for the case of axial symmetry and non-linear energy functionals, and solved with the help of a new parallel code. Formal properties of RPA theory are studied and special care is taken in order to validate the proper decoupling of spurious modes and their influence on the physical response. Sample applications to the magnetic and electric dipole transitions in $^{20}$Ne are presented and analyzed.
Quantum corrections to the Relativistic mean-field theory
Maydanyuk, Sergei P; Bakry, Ahmed
2016-01-01
In this paper, we compare the RMF theory and the model of deformed oscillator shells (DOS) in description of the quantum properties of the bound states of the spherically symmetric light nuclei. We obtain an explicit analytical relation between differential equations for the RMF theory and DOS model, which determine wave functions for nucleons. On such a basis we perform analysis of correspondence of quantum properties of nuclei. We find: (1) Potential $V_{RMF}$ of the RMF theory for nucleons has the wave functions $f$ and $g$ with joint part $h$ coincident exactly with the nucleon wave function of DOS model with potential $V_{\\rm shell}$. But, a difference between $V_{RMF}$ and $V_{\\rm shell}$ is essential for any nucleus. (2) The nucleon wave functions and densities obtained by the DOS and RMF theories are essentially different. The nucleon densities of the RMF theory contradict to knowledge about distribution of the proton and neutron densities inside the nuclei obtained from experimental data. This indica...
Pedestrian Flow in the Mean Field Limit
Haji Ali, Abdul Lateef
2012-11-01
We study the mean-field limit of a particle-based system modeling the behavior of many indistinguishable pedestrians as their number increases. The base model is a modified version of Helbing\\'s social force model. In the mean-field limit, the time-dependent density of two-dimensional pedestrians satisfies a four-dimensional integro-differential Fokker-Planck equation. To approximate the solution of the Fokker-Planck equation we use a time-splitting approach and solve the diffusion part using a Crank-Nicholson method. The advection part is solved using a Lax-Wendroff-Leveque method or an upwind Backward Euler method depending on the advection speed. Moreover, we use multilevel Monte Carlo to estimate observables from the particle-based system. We discuss these numerical methods, and present numerical results showing the convergence of observables that were calculated using the particle-based model as the number of pedestrians increases to those calculated using the probability density function satisfying the Fokker-Planck equation.
Mean field interaction in biochemical reaction networks
Tembine, Hamidou
2011-09-01
In this paper we establish a relationship between chemical dynamics and mean field game dynamics. We show that chemical reaction networks can be studied using noisy mean field limits. We provide deterministic, noisy and switching mean field limits and illustrate them with numerical examples. © 2011 IEEE.
Phillips, D R; Devine, N K
1998-01-01
The electromagnetic interactions of a relativistic two-body bound state are formulated in three dimensions using an equal-time (ET) formalism. This involves a systematic reduction of four-dimensional dynamics to a three-dimensional form by integrating out the time components of relative momenta. A conserved electromagnetic current is developed for the ET formalism. It is shown that consistent truncations of the electromagnetic current and the $NN$ interaction kernel may be made, order-by-order in the coupling constants, such that appropriate Ward-Takahashi identities are satisfied. A meson-exchange model of the $NN$ interaction is used to calculate deuteron vertex functions. Calculations of electromagnetic form factors for elastic scattering of electrons by deuterium are performed using an impulse-approximation current. Negative-energy components of the deuteron's vertex function and retardation effects in the meson-exchange interaction are found to have only minor effects on the deuteron form factors.
Alhalholy, Tareq
2016-01-01
Using the relativistic Eikonal approximation, we study the one and two photon exchange amplitudes in elastic electron-nucleon scattering for the case of transversely polarized nucleons with unpolarized electrons beam. In our approach, we utilize the convolution theory of Fourier transforms and the transverse charge density in transverse momentum space to evaluate the one and two photon exchange Eikonal amplitudes. The results obtained for the $2\\gamma$ amplitude in impact parameter space are compared to the corresponding 4D case. We show that while the one and two photon cross sections are azimuthally symmetric, the interference term between them is azimuthally asymmetric, which is an indication of an azimuthal single spin asymmetry for proton and neutron which can be attributed to the fact that the nucleon charge density is transversely (azimuthally) distorted in the transverse plane for transversely polarized nucleons. In addition, the calculations of the interference term for proton and neutron show agreem...
Mean Field Games for Stochastic Growth with Relative Utility
Huang, Minyi, E-mail: mhuang@math.carleton.ca [Carleton University, School of Mathematics and Statistics (Canada); Nguyen, Son Luu, E-mail: sonluu.nguyen@upr.edu [University of Puerto Rico, Department of Mathematics (United States)
2016-12-15
This paper considers continuous time stochastic growth-consumption optimization in a mean field game setting. The individual capital stock evolution is determined by a Cobb–Douglas production function, consumption and stochastic depreciation. The individual utility functional combines an own utility and a relative utility with respect to the population. The use of the relative utility reflects human psychology, leading to a natural pattern of mean field interaction. The fixed point equation of the mean field game is derived with the aid of some ordinary differential equations. Due to the relative utility interaction, our performance analysis depends on some ratio based approximation error estimate.
Variational Worldline Approximation for the Relativistic Two-Body Bound State in a Scalar Model
Barro-Bergfl"odt, K; Stingl, M
2006-01-01
We use the worldline representation of field theory together with a variational approximation to determine the lowest bound state in the scalar Wick-Cutkosky model where two equal-mass constituents interact via the exchange of mesons. Self-energy and vertex corrections are included approximately in a consistent way as well as crossed diagrams. Only vacuum-polarization effects of the heavy particles are neglected. In a path integral description of an appropriate current-current correlator an effective, retarded action is obtained by integrating out the meson field. As in the polaron problem we employ a quadratic trial action with variational functions to describe retardation and binding effects through multiple meson exchange.The variational equations for these functions are derived, discussed qualitatively and solved numerically. We compare our results with the ones from traditional approaches based on the Bethe-Salpeter equation and find an enhanced binding. For weak coupling this is worked out analytically ...
Deterministic Mean-Field Ensemble Kalman Filtering
Law, Kody J. H.
2016-05-03
The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. A density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence k between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d<2k. The fidelity of approximation of the true distribution is also established using an extension of the total variation metric to random measures. This is limited by a Gaussian bias term arising from nonlinearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
Worldline Variational Approximation: A New Approach to the Relativistic Binding Problem
Barro-Bergflodt, K; Stingl, M
2004-01-01
We determine the lowest bound-state pole of the density-density correlator in the scalar Wick-Cutkosky model where two equal-mass constituents interact via the exchange of mesons. This is done by employing the worldline representation of field theory together with a variational approximation as in Feynman's treatment of the polaron. Unlike traditional methods based on the Bethe-Salpeter equation, self-energy and vertex corrections are (approximately) included as are crossed diagrams. Only vacuum-polarization effects of the heavy particles are neglected. The well-known instability of the model due to self-energy effects leads to large qualitative and quantitative changes compared to traditional approaches which neglect them. We determine numerically the critical coupling constant above which no real solutions of the variational equations exist anymore and show that it is smaller than in the one-body case due to an induced instability. The width of the bound state above the critical coupling is estimated analyt...
The relativistic spherical δ -shell interaction in R3: Spectrum and approximation
Mas, Albert; Pizzichillo, Fabio
2017-08-01
This note revolves on the free Dirac operator in R3 and its δ -shell interaction with electrostatic potentials supported on a sphere. On one hand, we characterize the eigenstates of those couplings by finding sharp constants and minimizers of some precise inequalities related to an uncertainty principle. On the other hand, we prove that the domains given by Dittrich et al. [J. Math. Phys. 30(12), 2875-2882 (1989)] and by Arrizabalaga et al. [J. Math. Pures Appl. 102(4), 617-639 (2014)] for the realization of an electrostatic spherical shell interaction coincide. Finally, we explore the spectral relation between the shell interaction and its approximation by short range potentials with shrinking support, improving previous results in the spherical case.
Risk-sensitive mean-field games
Tembine, Hamidou
2014-04-01
In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost functional coincides with the value function satisfying a Hamilton -Jacobi- Bellman (HJB) equation with an additional quadratic term. We provide an explicit solution of the mean-field best response when the instantaneous cost functions are log-quadratic and the state dynamics are affine in the control. An equivalent mean-field risk-neutral problem is formulated and the corresponding mean-field equilibria are characterized in terms of backward-forward macroscopic McKean-Vlasov equations, Fokker-Planck-Kolmogorov equations, and HJB equations. We provide numerical examples on the mean field behavior to illustrate both linear and McKean-Vlasov dynamics. © 1963-2012 IEEE.
Kuroda, Takami; Takiwaki, Tomoya
2012-01-01
We present results from the first generation of multi-dimensional hydrodynamic core-collapse simulations in full general relativity (GR) that include an approximate treatment of neutrino transport. Using a M1 closure scheme with an analytic variable Eddington factor, we solve the energy-independent set of radiation energy and momentum based on the Thorne's momentum formalism. To simplify the source terms of the transport equations, a methodology of multiflavour neutrino leakage scheme is partly employed. Our newly developed code is designed to evolve the Einstein field equation together with the GR radiation hydrodynamic equations. We follow the dynamics starting from the onset of gravitational core-collapse of a 15 $M_{\\odot}$ star, through bounce, up to about 100 ms postbounce in this study to study how the spacial multi-dimensionality and GR would affect the dynamics in the early postbounce phase. Our 3D results support the anticipation in previous 1D results that the neutrino luminosity and average neutri...
Extended Deterministic Mean-Field Games
Gomes, Diogo A.
2016-04-21
In this paper, we consider mean-field games where the interaction of each player with the mean field takes into account not only the states of the players but also their collective behavior. To do so, we develop a random variable framework that is particularly convenient for these problems. We prove an existence result for extended mean-field games and establish uniqueness conditions. In the last section, we consider the Master Equation and discuss properties of its solutions.
Mean field approaches for $\\Xi^-$ hypernuclei and current experimental data
Sun, T T; Sagawa, H; Schulze, H -J; Meng, J
2016-01-01
Motivated by the recently observed hypernucleus (Kiso event) $^{15}_{\\Xi}$C ($^{14}$N$+\\Xi^-$), we identify the state of this system theoretically within the framework of the relativistic-mean-field and Skyrme-Hartree-Fock models. The $\\Xi N$ interactions are constructed to reproduce the two possibly observed $\\Xi^-$ removal energies, $4.38\\pm 0.25$ MeV or $1.11\\pm 0.25$ MeV. The present result is preferable to be $^{14}{\\rm N}({\\rm g.s.})+\\Xi^-(1p)$, corresponding to the latter value.
Mean Field Approach to the Giant Wormhole Problem
Gamba, A.; Kolokolov, I.; Martellini, M.
We introduce a gaussian probability density for the space-time distribution of worm-holes, thus taking effectively into account wormhole interaction. Using a mean-field approximation for the free energy, we show that giant wormholes are probabilistically suppressed in a homogenous isotropic “large” universe.
Critical fluctuations for quantum mean-field models
Fannes, M.; Kossakowski, A.; Verbeure, A. (Univ. Louvain (Belgium))
1991-11-01
A Ginzburg-Landau-type approximation is proposed for the local Gibbs states for quantum mean-field models that leads to the exact thermodynamics. Using this approach, the spin fluctuations are computed for some spin-1/2 models. At the critical temperature, the distribution function showing abnormal fluctuations is found explicitly.
Model-checking mean-field models: algorithms & applications
Kolesnichenko, Anna Victorovna
2014-01-01
Large systems of interacting objects are highly prevalent in today's world. In this thesis we primarily address such large systems in computer science. We model such large systems using mean-field approximation, which allows to compute the limiting behaviour of an infinite population of identical o
Optimized $\\delta$ expansion for relativistic nuclear models
Krein, G I; Peres-Menezes, D; Nielsen, M; Pinto, M B
1998-01-01
The optimized $\\delta$-expansion is a nonperturbative approach for field theoretic models which combines the techniques of perturbation theory and the variational principle. This technique is discussed in the $\\lambda \\phi^4$ model and then implemented in the Walecka model for the equation of state of nuclear matter. The results obtained with the $\\delta$ expansion are compared with those obtained with the traditional mean field, relativistic Hartree and Hartree-Fock approximations.
Bauso, Dario
2014-05-07
This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple\\'s network on their feeling states and their well-being. © 2014 Bauso et al.
Degenerate second order mean field games systems
Tonon, Daniela; Cardaliaguet, Pierre; Graber, Philip,; Poretta, Alessio
2014-01-01
Parallel session; International audience; We consider degenerate second order mean field games systems with a local coupling. The starting point is the idea that mean field games systems can be understood as an optimality condition for optimal control of PDEs. Developing this strategy for the degenerate second order case, we discuss the existence and uniqueness of a weak solution as well as its stability (vanishing viscosity limit). Speaker: Daniela TONON
Belendez, A [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Pascual, C [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E [Departamento de Optica, FarmacologIa y AnatomIa, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Neipp, C [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Belendez, T [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2008-02-15
A modified He's homotopy perturbation method is used to calculate higher-order analytical approximate solutions to the relativistic and Duffing-harmonic oscillators. The He's homotopy perturbation method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second-order linear differential equation, and so on. We find this modified homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. The approximate formulae obtained show excellent agreement with the exact solutions, and are valid for small as well as large amplitudes of oscillation, including the limiting cases of amplitude approaching zero and infinity. For the relativistic oscillator, only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate frequency of less than 1.6% for small and large values of oscillation amplitude, while this relative error is 0.65% for two iterations with two harmonics and as low as 0.18% when three harmonics are considered in the second approximation. For the Duffing-harmonic oscillator the relative error is as low as 0.078% when the second approximation is considered. Comparison of the result obtained using this method with those obtained by the harmonic balance methods reveals that the former is very effective and convenient.
Matveev, Alexei V; Rösch, Notker
2008-06-28
We suggest an approximate relativistic model for economical all-electron calculations on molecular systems that exploits an atomic ansatz for the relativistic projection transformation. With such a choice, the projection transformation matrix is by definition both transferable and independent of the geometry. The formulation is flexible with regard to the level at which the projection transformation is approximated; we employ the free-particle Foldy-Wouthuysen and the second-order Douglas-Kroll-Hess variants. The (atomic) infinite-order decoupling scheme shows little effect on structural parameters in scalar-relativistic calculations; also, the use of a screened nuclear potential in the definition of the projection transformation shows hardly any effect in the context of the present work. Applications to structural and energetic parameters of various systems (diatomics AuH, AuCl, and Au(2), two structural isomers of Ir(4), and uranyl dication UO(2) (2+) solvated by 3-6 water ligands) show that the atomic approximation to the conventional second-order Douglas-Kroll-Hess projection (ADKH) transformation yields highly accurate results at substantial computational savings, in particular, when calculating energy derivatives of larger systems. The size-dependence of the intrinsic error of the ADKH method in extended systems of heavy elements is analyzed for the atomization energies of Pd(n) clusters (n
Pion mean fields and heavy baryons
Yang, Ghil-Seok; Polyakov, Maxim V; Praszałowicz, Michał
2016-01-01
We show that the masses of the lowest-lying heavy baryons can be very well described in a pion mean-field approach. We consider a heavy baryon as a system consisting of the $N_c-1$ light quarks that induce the pion mean field, and a heavy quark as a static color source under the influence of this mean field. In this approach we derive a number of \\textit{model-independent} relations and calculate the heavy baryon masses using those of the lowest-lying light baryons as input. The results are in remarkable agreement with the experimental data. In addition, the mass of the $\\Omega_b^*$ baryon is predicted.
Mean Field Games with a Dominating Player
Bensoussan, A., E-mail: axb046100@utdallas.edu [The University of Texas at Dallas, International Center for Decision and Risk Analysis, Jindal School of Management (United States); Chau, M. H. M., E-mail: michaelchaumanho@gmail.com; Yam, S. C. P., E-mail: scpyam@sta.cuhk.edu.hk [The Chinese University of Hong Kong, Department of Statistics (Hong Kong, People’s Republic of China) (China)
2016-08-15
In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by the dominating player. We first provide the general theory and discuss the necessary condition for the optimal controls and equilibrium condition by adopting adjoint equation approach. We then present a special case in the context of linear-quadratic framework, in which a necessary and sufficient condition can be asserted by stochastic maximum principle; we finally establish the sufficient condition that guarantees the unique existence of the equilibrium control. The proof of the convergence result of finite player game to mean field counterpart is provided in Appendix.
Mean field games for cognitive radio networks
Tembine, Hamidou
2012-06-01
In this paper we study mobility effect and power saving in cognitive radio networks using mean field games. We consider two types of users: primary and secondary users. When active, each secondary transmitter-receiver uses carrier sensing and is subject to long-term energy constraint. We formulate the interaction between primary user and large number of secondary users as an hierarchical mean field game. In contrast to the classical large-scale approaches based on stochastic geometry, percolation theory and large random matrices, the proposed mean field framework allows one to describe the evolution of the density distribution and the associated performance metrics using coupled partial differential equations. We provide explicit formulas and algorithmic power management for both primary and secondary users. A complete characterization of the optimal distribution of energy and probability of success is given.
Dynamical mean-field theory from a quantum chemical perspective.
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.
Robust mean field games for coupled Markov jump linear systems
Moon, Jun; Başar, Tamer
2016-07-01
We consider robust stochastic large population games for coupled Markov jump linear systems (MJLSs). The N agents' individual MJLSs are governed by different infinitesimal generators, and are affected not only by the control input but also by an individual disturbance (or adversarial) input. The mean field term, representing the average behaviour of N agents, is included in the individual worst-case cost function to capture coupling effects among agents. To circumvent the computational complexity and analyse the worst-case effect of the disturbance, we use robust mean field game theory to design low-complexity robust decentralised controllers and to characterise the associated worst-case disturbance. We show that with the individual robust decentralised controller and the corresponding worst-case disturbance, which constitute a saddle-point solution to a generic stochastic differential game for MJLSs, the actual mean field behaviour can be approximated by a deterministic function which is a fixed-point solution to the constructed mean field system. We further show that the closed-loop system is uniformly stable independent of N, and an approximate optimality can be obtained in the sense of ε-Nash equilibrium, where ε can be taken to be arbitrarily close to zero as N becomes sufficiently large. A numerical example is included to illustrate the results.
Obstacle mean-field game problem
Gomes, Diogo A.
2015-01-01
In this paper, we introduce and study a first-order mean-field game obstacle problem. We examine the case of local dependence on the measure under assumptions that include both the logarithmic case and power-like nonlinearities. Since the obstacle operator is not differentiable, the equations for first-order mean field game problems have to be discussed carefully. Hence, we begin by considering a penalized problem. We prove this problem admits a unique solution satisfying uniform bounds. These bounds serve to pass to the limit in the penalized problem and to characterize the limiting equations. Finally, we prove uniqueness of solutions. © European Mathematical Society 2015.
Mean-field magnetohydrodynamics and dynamo theory
Krause, F
2013-01-01
Mean-Field Magnetohydrodynamics and Dynamo Theory provides a systematic introduction to mean-field magnetohydrodynamics and the dynamo theory, along with the results achieved. Topics covered include turbulence and large-scale structures; general properties of the turbulent electromotive force; homogeneity, isotropy, and mirror symmetry of turbulent fields; and turbulent electromotive force in the case of non-vanishing mean flow. The turbulent electromotive force in the case of rotational mean motion is also considered. This book is comprised of 17 chapters and opens with an overview of the gen
Buehring, W.
1983-03-01
Non-relativistic scattering phase shifts, bound state energies, and wave function normalization factors for a screened Coulomb potential of the Hulthen type are presented in the form of relatively simple analytic expressions. These formulae have been obtained by a suitable renormalization procedure applied to the quantities derived from an approximate Schroedinger equation which contains the exact Hulthen potential together with an approximate angular momentum term. When the screening exponent vanishes, our formulae reduce to the exact Coulomb expresions. The interrelation between our formulae and Pratt's analytic perturbation theory for screened Coulomb potentials' is discussed.
Caballero, J.A. [Univ. de Sevilla (Spain). Dept. de Fisica Atomica, Molecular y Nucl.]|[Instituto de Estructura de la Materia, Consejo Superior de Investigaciones Cientificas, Serrano 123, Madrid 28006 (Spain); Donnelly, T.W. [Centre for Theoretical Physics, Laboratory for Nuclear Science and Dept. of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139-4307 (United States); Moya de Guerra, E. [Instituto de Estructura de la Materia, Consejo Superior de Investigaciones Cientificas, Serrano 123, Madrid 28006 (Spain); Udias, J.M. [Departamento de Fisica Atomica, Molecular y Nuclear, Universidad Complutense de Madrid, Avda. Complutense s/n, Madrid 28040 (Spain)
1998-03-23
The issue of factorization within the context of coincidence quasi-elastic electron scattering is revisited. Using a relativistic formalism for the entire reaction mechanism and restricting ourselves to the case of plane waves for the outgoing proton, we discuss the role of the negative-energy components of the bound nucleon wave function. (orig.). 30 refs.
Amirkhanov, I V; Zhidkova, I E; Vasilev, S A
2000-01-01
Asymptotics of eigenfunctions and eigenvalues has been obtained for a singular perturbated relativistic analog of Schr`dinger equation. A singular convergence of asymptotic expansions of the boundary problems to degenerated problems is shown for a nonrelativistic Schr`dinger equation. The expansions obtained are in a good agreement with a numeric experiment.
Propagation peculiarities of mean field massive gravity
S. Deser
2015-10-01
Full Text Available 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 both 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. This applies both to m‾GR and mGR, and is a peculiar feature that is also problematic for consistent coupling to matter.
Thermal Effects in Dense Matter Beyond Mean Field Theory
Constantinou, Constantinos; Prakash, Madappa
2016-01-01
The formalism of next-to-leading order Fermi Liquid Theory is employed to calculate the thermal properties of symmetric nuclear and pure neutron matter in a relativistic many-body theory beyond the mean field level which includes two-loop effects. For all thermal variables, the semi-analytical next-to-leading order corrections reproduce results of the exact numerical calculations for entropies per baryon up to 2. This corresponds to excellent agreement down to sub-nuclear densities for temperatures up to $20$ MeV. In addition to providing physical insights, a rapid evaluation of the equation of state in the homogeneous phase of hot and dense matter is achieved through the use of the zero-temperature Landau effective mass function and its derivatives.
Dynamical mean field theory of optical third harmonic generation
Jafari, S. A.; Tohyama, T.; Maekawa, S.
2006-01-01
We formulate the third harmonic generation (THG) within the dynamical mean field theory (DMFT) approximation of the Hubbard model. In the limit of large dimensions, where DMFT becomes exact, the vertex corrections to current vertices are identically zero, and hence the calculation of the THG spectrum reduces to a time-ordered convolution, followd by appropriate analytic continuuation. We present the typical THG spectrum of the Hubbard model obtained by this method. Within our DMFT calculation...
Mean-field dynamo action in renovating shearing flows.
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.
A relativistic symmetry in nuclei
Ginocchio, J N [MS B283, Theoretical Division, Los Alamos National Laboratory Los Alamos, New Mexico 87545 (Mexico)
2007-11-15
We review some of the empirical and theoretical evidence supporting pseudospin symmetry in nuclei as a relativistic symmetry. We review the case that the eigenfunctions of realistic relativistic nuclear mean fields approximately conserve pseudospin symmetry in nuclei. We discuss the implications of pseudospin symmetry for magnetic dipole transitions and Gamow-Teller transitions between states in pseudospin doublets. We explore a more fundamental rationale for pseudospin symmetry in terms of quantum chromodynamics (QCD), the basic theory of the strong interactions. We show that pseudospin symmetry in nuclei implies spin symmetry for an anti-nucleon in a nuclear environment. We also discuss the future and what role pseudospin symmetry may be expected to play in an effective field theory of nucleons.
Mean-field and non-mean-field behaviors in scale-free networks with random Boolean dynamics
Castro e Silva, A [Departamento de Fisica, Universidade Federal de Ouro Preto, Campus Universitario, 35.400-000 Ouro Preto, Minas Gerais (Brazil); Kamphorst Leal da Silva, J, E-mail: alcidescs@gmail.co, E-mail: jaff@fisica.ufmg.b [Departamento de Fisica, Universidade Federal de Minas Gerais, Caixa Postal 702, 30.161-970, Belo Horizonte, Minas Gerais (Brazil)
2010-06-04
We study two types of simplified Boolean dynamics in scale-free networks, both with a synchronous update. Assigning only the Boolean functions AND and XOR to the nodes with probabilities 1 - p and p, respectively, we are able to analyze the density of 1's and the Hamming distance on the network by numerical simulations and by a mean-field approximation (annealed approximation). We show that the behavior is quite different if the node always enters in the dynamics as its own input (self-regulation) or not. The same conclusion holds for the Kauffman NK model. Moreover, the simulation results and the mean-field ones (i) agree well when there is no self-regulation and (ii) disagree for small p when self-regulation is present in the model.
Mean-Field and Non-Mean-Field Behaviors in Scale-free Networks with Random Boolean Dynamics
Silva, A Castro e
2009-01-01
We study two types of simplified Boolean dynamics over scale-free networks, both with synchronous update. Assigning only Boolean functions AND and XOR to the nodes with probability $1-p$ and $p$, respectively, we are able to analyze the density of 1's and the Hamming distance on the network by numerical simulations and by a mean-field approximation (annealed approximation). We show that the behavior is quite different if the node always enters in the dynamic as its own input (self-regulation) or not. The same conclusion holds for the Kauffman KN model. Moreover, the simulation results and the mean-field ones (i) agree well when there is no self-regulation, and (ii) disagree for small $p$ when self-regulation is present in the model.
Mean-field learning for satisfactory solutions
Tembine, Hamidou
2013-12-01
One of the fundamental challenges in distributed interactive systems is to design efficient, accurate, and fair solutions. In such systems, a satisfactory solution is an innovative approach that aims to provide all players with a satisfactory payoff anytime and anywhere. In this paper we study fully distributed learning schemes for satisfactory solutions in games with continuous action space. Considering games where the payoff function depends only on own-action and an aggregate term, we show that the complexity of learning systems can be significantly reduced, leading to the so-called mean-field learning. We provide sufficient conditions for convergence to a satisfactory solution and we give explicit convergence time bounds. Then, several acceleration techniques are used in order to improve the convergence rate. We illustrate numerically the proposed mean-field learning schemes for quality-of-service management in communication networks. © 2013 IEEE.
Mean field methods for cortical network dynamics
Hertz, J.; Lerchner, Alexander; Ahmadi, M.
2004-01-01
We review the use of mean field theory for describing the dynamics of dense, randomly connected cortical circuits. For a simple network of excitatory and inhibitory leaky integrate- and-fire neurons, we can show how the firing irregularity, as measured by the Fano factor, increases with the stren...... cortex. Finally, an extension of the model to describe an orientation hypercolumn provides understanding of how cortical interactions sharpen orientation tuning, in a way that is consistent with observed firing statistics...
Bosonic Dynamical Mean-Field Theory
Snoek, Michiel; Hofstetter, Walter
2013-02-01
We derive the bosonic dynamical mean-field equations for bosonic atoms in optical lattices with arbitrary lattice geometry. The equations are presented as a systematic expansion in 1/z, z being the number of lattice neighbours. Hence the theory is applicable in sufficiently high-dimensional lattices. We apply the method to a two-component mixture, for which a rich phase diagram with spin order is revealed.
Mean field games systems of first order
Cardaliaguet, Pierre; Graber, Philip Jameson
2014-01-01
International audience; We consider a system of mean field games with local coupling in the deterministic limit. Under general structure conditions on the Hamiltonian and coupling, we prove existence and uniqueness of the weak solution, characterizing this solution as the minimizer of some optimal control of Hamilton-Jacobi and continuity equations. We also prove that this solution converges in the long time average to the solution of the associated ergodic problem.
'Phase diagram' of a mean field game
Swiecicki, Igor; Ullmo, Denis
2015-01-01
Mean field games were introduced by J-M.Lasry and P-L. Lions in the mathematical community, and independently by M. Huang and co-workers in the engineering community, to deal with optimization problems when the number of agents becomes very large. In this article we study in detail a particular example called the 'seminar problem' introduced by O.Gu\\'eant, J-M Lasry, and P-L. Lions in 2010. This model contains the main ingredients of any mean field game but has the particular feature that all agent are coupled only through a simple random event (the seminar starting time) that they all contribute to form. In the mean field limit, this event becomes deterministic and its value can be fixed through a self consistent procedure. This allows for a rather thorough understanding of the solutions of the problem, through both exact results and a detailed analysis of various limiting regimes. For a sensible class of initial configurations, distinct behaviors can be associated to different domains in the parameter space...
Dynamical mean-field theory for quantum chemistry.
Lin, Nan; Marianetti, C A; Millis, Andrew J; Reichman, David R
2011-03-04
The dynamical mean-field concept of approximating an unsolvable many-body problem in terms of the solution of an auxiliary quantum impurity problem, introduced to study bulk materials with a continuous energy spectrum, is here extended to molecules, i.e., finite systems with a discrete energy spectrum. The application to small clusters of hydrogen atoms yields ground state energies which are competitive with leading quantum chemical approaches at intermediate and large interatomic distances as well as good approximations to the excitation spectrum.
Time-odd mean fields in covariant density functional theory: Rotating systems
Afanasjev, A V; 10.1103/PhysRev.82.034329
2010-01-01
Time-odd mean fields (nuclear magnetism) and their impact on physical observables in rotating nuclei are studied in the framework of covariant density functional theory (CDFT). It is shown that they have profound effect on the dynamic and kinematic moments of inertia. Particle number, configuration and rotational frequency dependences of their impact on the moments of inertia have been analysed in a systematic way. Nuclear magnetism can also considerably modify the band crossing features such as crossing frequencies and the properties of the kinematic and dynamic moments of inertia in the band crossing region. The impact of time-odd mean fields on the moments of inertia in the regions away from band crossing only weakly depends on the relativistic mean field parametrization, reflecting good localization of the properties of time-odd mean fields in CDFT. The moments of inertia of normal-deformed nuclei considerably deviate from the rigid body value. On the contrary, superdeformed and hyperdeformed nuclei have ...
Mean field methods for cortical network dynamics
Hertz, J.; Lerchner, Alexander; Ahmadi, M.
2004-01-01
We review the use of mean field theory for describing the dynamics of dense, randomly connected cortical circuits. For a simple network of excitatory and inhibitory leaky integrate- and-fire neurons, we can show how the firing irregularity, as measured by the Fano factor, increases...... with the strength of the synapses in the network and with the value to which the membrane potential is reset after a spike. Generalizing the model to include conductance-based synapses gives insight into the connection between the firing statistics and the high- conductance state observed experimentally in visual...
Mean-field behavior of cluster dynamics
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.
Resummed mean-field inference for strongly coupled data
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.
Mean field magnetization of gapped anisotropic multiplet
Paixão, L. S.; Reis, M. S.
2014-06-01
Some materials have a large gap between the ground and first excited states. At temperatures smaller than the gap value, the thermodynamic properties of such materials are mainly ruled by the ground state. It is also common to find materials with magnetocrystalline anisotropy, which arises due to interatomic interactions. The present paper uses a classical approach to deal large angular momenta in such materials. Based on analytical expressions for the thermodynamics of paramagnetic gapped anisotropic multiplets, we use mean field theory to study the influence of the anisotropy upon the properties of interacting systems. We also use Landau theory to determine the influence of the anisotropy in first and second order phase transitions. It is found that the anisotropy increases the critical temperature, and enlarges the hysteresis of first order transitions. We present analytical expressions for the quantities analyzed.
Invisible dynamo in mean-field models
Reshetnyak, M. Yu.
2016-07-01
The inverse problem in a spherical shell to find the two-dimensional spatial distributions of the α-effect and differential rotation in a mean-field dynamo model has been solved. The derived distributions lead to the generation of a magnetic field concentrated inside the convection zone. The magnetic field is shown to have no time to rise from the region of maximum generation located in the lower layers to the surface in the polarity reversal time due to magnetic diffusion. The ratio of the maximum magnetic energy in the convection zone to its value at the outer boundary reaches two orders of magnitude or more. This result is important in interpreting the observed stellar and planetary magnetic fields. The proposed method of solving the inverse nonlinear dynamo problem is easily adapted for a wide class of mathematical-physics problems.
Mean-field models for disordered crystals
Cancès, Eric; Lewin, Mathieu
2012-01-01
In this article, we set up a functional setting for mean-field electronic structure models of Hartree-Fock or Kohn-Sham types for disordered crystals. The electrons are quantum particles and the nuclei are classical point-like articles whose positions and charges are random. We prove the existence of a minimizer of the energy per unit volume and the uniqueness of the ground state density of such disordered crystals, for the reduced Hartree-Fock model (rHF). We consider both (short-range) Yukawa and (long-range) Coulomb interactions. In the former case, we prove in addition that the rHF ground state density matrix satisfies a self-consistent equation, and that our model for disordered crystals is the thermodynamic limit of the supercell model.
Fictive impurity approach to dynamical mean field theory
Fuhrmann, A.
2006-10-15
A new extension of the dynamical mean-field theory was investigated in the regime of large Coulomb repulsion. A number of physical quantities such as single-particle density of states, spin-spin correlation, internal energy and Neel temperature, were computed for a two-dimensional Hubbard model at half-filling. The numerical data were compared to our analytical results as well as to the results computed using the dynamical cluster approximation. In the second part of this work we consider a two-plane Hubbard model. The transport properties of the bilayer were investigated and the phase diagram was obtained. (orig.)
Mean Field Evolution of Fermions with Coulomb Interaction
Porta, Marcello; Rademacher, Simone; Saffirio, Chiara; Schlein, Benjamin
2017-03-01
We study the many body Schrödinger evolution of weakly coupled fermions interacting through a Coulomb potential. We are interested in a joint mean field and semiclassical scaling, that emerges naturally for initially confined particles. For initial data describing approximate Slater determinants, we prove convergence of the many-body evolution towards Hartree-Fock dynamics. Our result holds under a condition on the solution of the Hartree-Fock equation, that we can only show in a very special situation (translation invariant data, whose Hartree-Fock evolution is trivial), but that we expect to hold more generally.
Time dependent mean-field games
Gomes, Diogo A.
2014-01-06
We consider time dependent mean-field games (MFG) with a local power-like dependence on the measure and Hamiltonians satisfying both sub and superquadratic growth conditions. We establish existence of smooth solutions under a certain set of conditions depending both on the growth of the Hamiltonian as well as on the dimension. In the subquadratic case this is done by combining a Gagliardo-Nirenberg type of argument with a new class of polynomial estimates for solutions of the Fokker-Planck equation in terms of LrLp- norms of DpH. These techniques do not apply to the superquadratic case. In this setting we recur to a delicate argument that combines the non-linear adjoint method with polynomial estimates for solutions of the Fokker-Planck equation in terms of L1L1-norms of DpH. Concerning the subquadratic case, we substantially improve and extend the results previously obtained. Furthermore, to the best of our knowledge, the superquadratic case has not been addressed in the literature yet. In fact, it is likely that our estimates may also add to the current understanding of Hamilton-Jacobi equations with superquadratic Hamiltonians.
Nonequilibrium dynamical mean-field theory
Eckstein, Martin
2009-12-21
The aim of this thesis is the investigation of strongly interacting quantum many-particle systems in nonequilibrium by means of the dynamical mean-field theory (DMFT). An efficient numerical implementation of the nonequilibrium DMFT equations within the Keldysh formalism is provided, as well a discussion of several approaches to solve effective single-site problem to which lattice models such as the Hubbard-model are mapped within DMFT. DMFT is then used to study the relaxation of the thermodynamic state after a sudden increase of the interaction parameter in two different models: the Hubbard model and the Falicov-Kimball model. In the latter case an exact solution can be given, which shows that the state does not even thermalize after infinite waiting times. For a slow change of the interaction, a transition to adiabatic behavior is found. The Hubbard model, on the other hand, shows a very sensitive dependence of the relaxation on the interaction, which may be called a dynamical phase transition. Rapid thermalization only occurs at the interaction parameter which corresponds to this transition. (orig.)
Time-odd mean fields in the rotating frame microscopic nature of nuclear magnetism
Afanasiev, A V
2000-01-01
The microscopic role of nuclear magnetism in rotating frame is investigated for the first time in the framework of the cranked relativistic mean field theory. It is shown that nuclear magnetism modifies the expectation values of single-particle spin, orbital and total angular momenta along the rotational axis effectively creating additional angular momentum. This effect leads to the increase of kinematic and dynamic moments of inertia at given rotational frequency and has an impact on effective alignments.
Shell Effect of Superheavy Nuclei in Self-consistent Mean-Field Models
RENZhong-Zhou; TAIFei; XUChang; CHENDing-Han; ZHANGHu-Yong; CAIXiang-Zhou; SHENWen-Qing
2004-01-01
We analyze in detail the numerical results of superheavy nuclei in deformed relativistic mean-field model and deformed Skyrme-Hartree-Fock model. The common points and differences of both models are systematically compared and discussed. Their consequences on the stability of superheavy nuclei are explored and explained. The theoreticalresults are compared with new data of superheavy nuclei from GSI and from Dubna and reasonable agreement is reached.Nuclear shell effect in superheavy region is analyzed and discussed. The spherical shell effect disappears in some cases due to the appearance of deformation or superdeformation in the ground states of nuclei, where valence nucleons occupysignificantly the intruder levels of nuclei. It is shown for the first time that the significant occupation of vaJence nucleons on the intruder states plays an important role for the ground state properties of superheavy nuclei. Nuclei are stable in the deformed or superdeformed configurations. We further point out that one cannot obtain the octupole deformation of even-even nuclei in the present relativistic mean-field model with the σ，ω and ρ mesons because there is no parityviolating interaction and the conservation of parity of even-even nuclei is a basic assumption of the present relativistic mean-field model.
MALFLIET, R
1993-01-01
We discuss the present status of relativistic transport theory. Special emphasis is put on problems of topical interest: hadronic features, thermodynamical consistent approximations and spectral properties.
Control and Nash Games with Mean Field Effect
Alain BENSOUSSAN; Jens FREHSE
2013-01-01
Mean field theory has raised a lot of interest in the recent years (see in particular the results of Lasry-Lions in 2006 and 2007,of Gueant-Lasry-Lions in 2011,of HuangCaines-Malham in 2007 and many others).There are a lot of applications.In general,the applications concern approximating an infinite number of players with common behavior by a representative agent.This agent has to solve a control problem perturbed by a field equation,representing in some way the behavior of the average infinite number of agents.This approach does not lead easily to the problems of Nash equilibrium for a finite number of players,perturbed by field equations,unless one considers averaging within different groups,which has not been done in the literature,and seems quite challenging.In this paper,the authors approach similar problems with a different motivation which makes sense for control and also for differential games.Thus the systems of nonlinear partial differential equations with mean field terms,which have not been addressed in the literature so far,are considered here.
Topological properties of the mean-field ϕ4 model
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.
Mean-field vs. Stochastic Models for Transcriptional Regulation
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.
Mean-field versus stochastic models for transcriptional regulation
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.
Two stochastic mean-field polycrystal plasticity methods
Tonks, Michael [Los Alamos National Laboratory
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.
Modeling distributed axonal delays in mean-field brain dynamics
Roberts, J. A.; Robinson, P. A.
2008-11-01
The range of conduction delays between connected neuronal populations is often modeled as a single discrete delay, assumed to be an effective value averaging over all fiber velocities. This paper shows the effects of distributed delays on signal propagation. A distribution acts as a linear filter, imposing an upper frequency cutoff that is inversely proportional to the delay width. Distributed thalamocortical and corticothalamic delays are incorporated into a physiologically based mean-field model of the cortex and thalamus to illustrate their effects on the electroencephalogram (EEG). The power spectrum is acutely sensitive to the width of the thalamocortical delay distribution, and more so than the corticothalamic distribution, because all input signals must travel along the thalamocortical pathway. This imposes a cutoff frequency above which the spectrum is overly damped. The positions of spectral peaks in the resting EEG depend primarily on the distribution mean, with only weak dependences on distribution width. Increasing distribution width increases the stability of fixed point solutions. A single discrete delay successfully approximates a distribution for frequencies below a cutoff that is inversely proportional to the delay width, provided that other model parameters are moderately adjusted. A pair of discrete delays together having the same mean, variance, and skewness as the distribution approximates the distribution over the same frequency range without needing parameter adjustment. Delay distributions with large fractional widths are well approximated by low-order differential equations.
Some Aspects of Nuclear Structure in Relativistic Approach
MAZhong-Yu; RONGJian; CAOLi-Gang; CHENBao-Qiu; LIULing
2004-01-01
The nucleon effective interaction in the nuclear medium is investigated in the framework of the DiracBrueckner-Hartree-Fock (DBHF) approach. A new decomposition of the Dirac structure of nucleon self-energy in the DBHF is adopted for asymmetric nuclear matter. The properties of finite nuclei are investigated with the nucleon effective interaction. The agreement with the experimental data is satisfactory. The relativistic microscopic optical potential in asymmetric nuclear matter is investigated in the DBHF approach. The proton scattering from nuclei is calculated and compared with the experimental data. A proper treatment of the resonant continuum for exotic nuclei is studied. The width effect of the resonant continuum on the pairing correlation is discussed. The quasiparticle relativistic random phase approximation based on the relativistic mean-field ground state in the response function formalism is also addressed.
Relativistic models for quasielastic electron and neutrino-nucleus scattering
Meucci Andrea
2012-12-01
Full Text Available Relativistic models developed within the framework of the impulse approximation for quasielastic (QE electron scattering and successfully tested in comparison with electron-scattering data have been extended to neutrino-nucleus scattering. Different descriptions of final-state interactions (FSI in the inclusive scattering are compared. In the relativistic Green’s function (RGF model FSI are described consistently with the exclusive scattering using a complex optical potential. In the relativistic mean field (RMF model FSI are described by the same RMF potential which gives the bound states. The results of the models are compared for electron and neutrino scattering and, for neutrino scattering, with the recently measured charged-current QE (CCQE MiniBooNE cross sections.
Dual mean field search for large scale linear and quadratic knapsack problems
Banda, Juan; Velasco, Jonás; Berrones, Arturo
2017-07-01
An implementation of mean field annealing to deal with large scale linear and non linear binary optimization problems is given. Mean field annealing is based on the analogy between combinatorial optimization and interacting physical systems at thermal equilibrium. Specifically, a mean field approximation of the Boltzmann distribution given by a Lagrangian that encompass the objective function and the constraints is calculated. The original discrete task is in this way transformed into a continuous variational problem. In our version of mean field annealing, no temperature parameter is used, but a good starting point in the dual space is given by a ;thermodynamic limit; argument. The method is tested in linear and quadratic knapsack problems with sizes that are considerably larger than those used in previous studies of mean field annealing. Dual mean field annealing is capable to find high quality solutions in running times that are orders of magnitude shorter than state of the art algorithms. Moreover, as may be expected for a mean field theory, the solutions tend to be more accurate as the number of variables grow.
Haba, Z
2009-02-01
We discuss relativistic diffusion in proper time in the approach of Schay (Ph.D. thesis, Princeton University, Princeton, NJ, 1961) and Dudley [Ark. Mat. 6, 241 (1965)]. We derive (Langevin) stochastic differential equations in various coordinates. We show that in some coordinates the stochastic differential equations become linear. We obtain momentum probability distribution in an explicit form. We discuss a relativistic particle diffusing in an external electromagnetic field. We solve the Langevin equations in the case of parallel electric and magnetic fields. We derive a kinetic equation for the evolution of the probability distribution. We discuss drag terms leading to an equilibrium distribution. The relativistic analog of the Ornstein-Uhlenbeck process is not unique. We show that if the drag comes from a diffusion approximation to the master equation then its form is strongly restricted. The drag leading to the Tsallis equilibrium distribution satisfies this restriction whereas the one of the Jüttner distribution does not. We show that any function of the relativistic energy can be the equilibrium distribution for a particle in a static electric field. A preliminary study of the time evolution with friction is presented. It is shown that the problem is equivalent to quantum mechanics of a particle moving on a hyperboloid with a potential determined by the drag. A relation to diffusions appearing in heavy ion collisions is briefly discussed.
Nonequilibrium Dynamical Mean-Field Theory for Bosonic Lattice Models
2015-01-01
We develop the nonequilibrium extension of bosonic dynamical mean-field theory and a Nambu real-time strong-coupling perturbative impurity solver. In contrast to Gutzwiller mean-field theory and strong-coupling perturbative approaches, nonequilibrium bosonic dynamical mean-field theory captures not only dynamical transitions but also damping and thermalization effects at finite temperature. We apply the formalism to quenches in the Bose-Hubbard model, starting from both the normal and the Bos...
Verbalization of Mean Field Utterances in German Instructions
Tayupova O. I.
2013-01-01
Full Text Available The article investigates ways of actualization of mean field utterances used in modern German instructions considering the type of the text. The author determines and analyzes similarities and differences in linguistic means used in mean field utterances in the context of such text subtypes as instructions to household appliances, cosmetic products directions and prescribing information for pharmaceutical drugs use.
Nuclear mean field from chiral pion-nucleon dynamics
Kaiser, N; Weise, W
2002-01-01
Using the two-loop approximation of chiral perturbation theory, we calculate the momentum- and density-dependent single-particle potential of nucleons in isospin-symmetric nuclear matter. The contributions from one- and two-pion exchange diagrams give rise to a potential depth for a nucleon at rest of U(0,k sub f sub 0)=-53.2 MeV at saturation density. The momentum dependence of the real part of the single-particle potential U(p,k sub f sub 0) is nonmonotonic and can be translated into a mean effective nucleon mass of M*bar approx =0.8M. The imaginary part of the single-particle potential W(p,k sub f) is generated to that order entirely by iterated one-pion exchange. The resulting half width of a nucleon hole-state at the bottom of the Fermi sea comes out as W(0,k sub f sub 0)=29.7 MeV. The basic theorems of Hugenholtz-Van-Hove and Luttinger are satisfied in our perturbative two-loop calculation of the nuclear mean field.
On Social Optima of Non-Cooperative Mean Field Games
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.
Mean field dynamics of networks of delay-coupled noisy excitable units
Franović, Igor, E-mail: franovic@ipb.ac.rs [Scientific Computing Laboratory, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade (Serbia); Todorović, Kristina; Burić, Nikola [Department of Physics and Mathematics, Faculty of Pharmacy, University of Belgrade, Vojvode Stepe 450, Belgrade (Serbia); Vasović, Nebojša [Department of Applied Mathematics, Faculty of Mining and Geology, University of Belgrade, PO Box 162, Belgrade (Serbia)
2016-06-08
We use the mean-field approach to analyze the collective dynamics in macroscopic networks of stochastic Fitzhugh-Nagumo units with delayed couplings. The conditions for validity of the two main approximations behind the model, called the Gaussian approximation and the Quasi-independence approximation, are examined. It is shown that the dynamics of the mean-field model may indicate in a self-consistent fashion the parameter domains where the Quasi-independence approximation fails. Apart from a network of globally coupled units, we also consider the paradigmatic setup of two interacting assemblies to demonstrate how our framework may be extended to hierarchical and modular networks. In both cases, the mean-field model can be used to qualitatively analyze the stability of the system, as well as the scenarios for the onset and the suppression of the collective mode. In quantitative terms, the mean-field model is capable of predicting the average oscillation frequency corresponding to the global variables of the exact system.
Mean-field Approach to the Derivation of Baryon Superpotential from Matrix Model
Suzuki, H
2003-01-01
We discuss how to obtain the superpotential of the baryons and mesons for SU(N) gauge theories with N flavour matter fields from matrix integral. We apply the mean-field approximation for the matrix integral. Assuming the planar limit of the self-consistency equation, we show that the result almost agrees with the field theoretical result.
Analytically Solvable Mean-Field Potential for Stable and Exotic Nuclei
Stoitsov, M. V.; S. S. Dimitrova(INRNE, Sofia); Pittel, S.; Van Isacker, P.(GANIL, CEA/DSM–CNRS/IN2P3, Bd Henri Becquerel, BP 55027, F-14076 Caen Cedex 5, France); Frank, A
1997-01-01
Slater determinants built from the single-particle wave functions of the analytically solvable Ginocchio potential are used to approximate the self-consistent Hartree-Fock solutions for the ground states of nuclei. The results indicate that the Ginocchio potential provides a good parametrization of the nuclear mean field for a wide range of nuclei, including those at the limit of particle stability.
Mean field dynamics of networks of delay-coupled noisy excitable units
Franović, Igor; Todorović, Kristina; Vasović, Nebojša; Burić, Nikola
2016-06-01
We use the mean-field approach to analyze the collective dynamics in macroscopic networks of stochastic Fitzhugh-Nagumo units with delayed couplings. The conditions for validity of the two main approximations behind the model, called the Gaussian approximation and the Quasi-independence approximation, are examined. It is shown that the dynamics of the mean-field model may indicate in a self-consistent fashion the parameter domains where the Quasi-independence approximation fails. Apart from a network of globally coupled units, we also consider the paradigmatic setup of two interacting assemblies to demonstrate how our framework may be extended to hierarchical and modular networks. In both cases, the mean-field model can be used to qualitatively analyze the stability of the system, as well as the scenarios for the onset and the suppression of the collective mode. In quantitative terms, the mean-field model is capable of predicting the average oscillation frequency corresponding to the global variables of the exact system.
Mean-field instabilities and cluster formation in nuclear reactions
Colonna, M; Baran, V
2016-01-01
We review recent results on intermediate mass cluster production in heavy ion collisions at Fermi energy and in spallation reactions. Our studies are based on modern transport theories, employing effective interactions for the nuclear mean-field and incorporating two-body correlations and fluctuations. Namely we will consider the Stochastic Mean Field (SMF) approach and the recently developed Boltzmann-Langevin One Body (BLOB) model. We focus on cluster production emerging from the possible occurrence of low-density mean-field instabilities in heavy ion reactions. Within such a framework, the respective role of one and two-body effects, in the two models considered, will be carefully analysed. We will discuss, in particular, fragment production in central and semi-peripheral heavy ion collisions, which is the object of many recent experimental investigations. Moreover, in the context of spallation reactions, we will show how thermal expansion may trigger the development of mean-field instabilities, leading to...
Mean Field Games Models-A Brief Survey
Gomes, Diogo A.
2013-11-20
The mean-field framework was developed to study systems with an infinite number of rational agents in competition, which arise naturally in many applications. The systematic study of these problems was started, in the mathematical community by Lasry and Lions, and independently around the same time in the engineering community by P. Caines, Minyi Huang, and Roland Malhamé. Since these seminal contributions, the research in mean-field games has grown exponentially, and in this paper we present a brief survey of mean-field models as well as recent results and techniques. In the first part of this paper, we study reduced mean-field games, that is, mean-field games, which are written as a system of a Hamilton-Jacobi equation and a transport or Fokker-Planck equation. We start by the derivation of the models and by describing some of the existence results available in the literature. Then we discuss the uniqueness of a solution and propose a definition of relaxed solution for mean-field games that allows to establish uniqueness under minimal regularity hypothesis. A special class of mean-field games that we discuss in some detail is equivalent to the Euler-Lagrange equation of suitable functionals. We present in detail various additional examples, including extensions to population dynamics models. This section ends with a brief overview of the random variables point of view as well as some applications to extended mean-field games models. These extended models arise in problems where the costs incurred by the agents depend not only on the distribution of the other agents, but also on their actions. The second part of the paper concerns mean-field games in master form. These mean-field games can be modeled as a partial differential equation in an infinite dimensional space. We discuss both deterministic models as well as problems where the agents are correlated. We end the paper with a mean-field model for price impact. © 2013 Springer Science+Business Media New York.
Streamlined mean field variational Bayes for longitudinal and multilevel data analysis.
Lee, Cathy Yuen Yi; Wand, Matt P
2016-07-01
Streamlined mean field variational Bayes algorithms for efficient fitting and inference in large models for longitudinal and multilevel data analysis are obtained. The number of operations is linear in the number of groups at each level, which represents a two orders of magnitude improvement over the naïve approach. Storage requirements are also lessened considerably. We treat models for the Gaussian and binary response situations. Our algorithms allow the fastest ever approximate Bayesian analyses of arbitrarily large longitudinal and multilevel datasets, with little degradation in accuracy compared with Markov chain Monte Carlo. The modularity of mean field variational Bayes allows relatively simple extension to more complicated scenarios.
Frank, T. D.; Daffertshofer, A.; Beek, P. J.
2001-01-01
We study the transient and stationary behavior of many-particle systems in terms of multivariate Ornstein-Uhlenbeck processes with friction and diffusion coefficients that depend nonlinearly on process mean fields. Mean-field approximations of this kind of system are derived in terms of Fokker-Planck equations. In such systems, multiple stationary solutions as well as bifurcations of stationary solutions may occur. In addition, strictly monotonically decreasing steady-state autocorrelation functions that decay faster than exponential functions are found, which are used to describe the erratic motion of the center of pressure during quiet standing.
Calculating charge-carrier mobilities in disordered semiconducting polymers: Mean field and beyond
Cottaar, J.; Bobbert, P. A.
2006-09-01
We model charge transport in disordered semiconducting polymers by hopping of charges on a regular cubic lattice of sites. A large on-site Coulomb repulsion prohibits double occupancy of the sites. Disorder is introduced by taking random site energies from a Gaussian distribution. Recently, it was demonstrated that this model leads to a dependence of the charge-carrier mobilities on the density of charge carriers that is in agreement with experimental observations. The model is conveniently solved within a mean-field approximation, in which the correlation between the occupational probabilities of different sites is neglected. This approximation becomes exact in the limit of vanishing charge-carrier densities, but needs to be checked at high densities. We perform this check by dividing the lattice in pairs of neighboring sites and taking into account the correlation between the sites within each pair explicitly. This pair approximation is expected to account for the most important corrections to the mean-field approximation. We study the effects of varying temperature, charge-carrier density, and electric field. We demonstrate that in the parameter regime relevant for semiconducting polymers used in practical devices the corrections to the mobilities calculated from the mean-field approximation will not exceed a few percent, so that this approximation can be safely used.
Mean field theories and dual variation mathematical structures of the mesoscopic model
Suzuki, Takashi
2015-01-01
Mean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory, plasma physics, quantum chemistry, mathematical oncology, non-equilibirum thermodynamics. spite of such a wide range of scientific areas that are concerned with the mean field theory, a unified study of its mathematical structure has not been discussed explicitly in the open literature. The benefit of this point of view on nonlinear problems should have significant impact on future research, as will be seen from the underlying features of self-assembly or bottom-up self-organization which is to be illustrated in a unified way. The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics.
Nuclear matter properties in the relativistic mean field model with $\\sigma-\\omega$ coupling
Chung, K C; Santiago, A J; Zhang, J W
2001-01-01
The possibility of extending the linear sigma-omega model by introducing a sigma-omega coupling phenomenologically is explored. It is shown that, in contrast to the usual Walecka model, not only the effective nucleon mass M* but also the effective sigma meson mass m*_sigma and the effective omega meson mass m*_omega are nucleon density dependent. When the model parameters are fitted to the nuclear saturation point (the nuclear radius constant r_0=1.14fm and volume energy a_1=16.0MeV) as well as to the effective nucleon mass M*=0.85M, the model yields m*_sigma=1.09m_sigma and m*_omega=0.90m_omega at the saturation point, and the nuclear incompressibility K_0=501MeV. The lowest value of K_0 given by this model by adjusting the model parameters is around 227MeV.
Deformed neutron stars due to strong magnetic field in terms of relativistic mean field theories
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.
Mean-field diffusivities in passive scalar and magnetic transport in irrotational flows
Rädler, Karl-Heinz; Del Sordo, Fabio; Rheinhardt, Matthias
2011-01-01
Certain aspects of the mean-field theory of turbulent passive scalar transport and of mean-field electrodynamics are considered with particular emphasis on aspects of compressible fluids. It is demonstrated that the total mean-field diffusivity for passive scalar transport in a compressible flow may well be smaller than the molecular diffusivity. This is in full analogy to an old finding regarding the magnetic mean-field diffusivity in an electrically conducting turbulently moving compressible fluid. These phenomena occur if the irrotational part of the motion dominates the vortical part, the P\\'eclet or magnetic Reynolds numbers are not too large and, in addition, the variation of the flow pattern is slow. For both the passive scalar and the magnetic case several further analytical results on mean-field diffusivities and related quantities found within the second-order correlation approximation are presented as well as numerical results obtained by the test-field method, which applies independently of this a...
Uncertainty quantification for mean field games in social interactions
Dia, Ben Mansour
2016-01-09
We present an overview of mean field games formulation. A comparative analysis of the optimality for a stochastic McKean-Vlasov process with time-dependent probability is presented. Then we examine mean-field games for social interactions and we show that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize couple (marriage). However , if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. Finally we introduce the Wiener chaos expansion for the construction of solution of stochastic differential equations of Mckean-Vlasov type. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and allow to quantify the uncertainty in the optimality system.
Regularity theory for mean-field game systems
Gomes, Diogo A; Voskanyan, Vardan
2016-01-01
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.
Accretion Disks and Dynamos: Toward a Unified Mean Field Theory
Blackman, Eric G
2012-01-01
Conversion of gravitational energy into radiation near stars and compact objects in accretion disks the origin of large scale magnetic fields in astrophysical rotators have long been distinct topics of active research in astrophysics. In semi-analytic work on both problems it has been useful to presume large scale symmetries, which necessarily results in mean field theories; magnetohydrodynamic turbulence makes the underlying systems locally asymmetric and highly nonlinear. Synergy between theory and simulations should aim for the development of practical, semi-analytic mean field models that capture the essential physics and can be used for observational modeling. Mean field dynamo (MFD) theory and alpha-viscosity accretion disc theory have exemplified such distinct pursuits. Both are presently incomplete, but 21st century MFD theory has nonlinear predictive power compared to 20th century MFD. in contrast, alpha-viscosity accretion theory is still in a 20th century state. In fact, insights from MFD theory ar...
Nonequilibrium Dynamical Mean-Field Theory for Bosonic Lattice Models
Strand, Hugo U. R.; Eckstein, Martin; Werner, Philipp
2015-01-01
We develop the nonequilibrium extension of bosonic dynamical mean-field theory and a Nambu real-time strong-coupling perturbative impurity solver. In contrast to Gutzwiller mean-field theory and strong-coupling perturbative approaches, nonequilibrium bosonic dynamical mean-field theory captures not only dynamical transitions but also damping and thermalization effects at finite temperature. We apply the formalism to quenches in the Bose-Hubbard model, starting from both the normal and the Bose-condensed phases. Depending on the parameter regime, one observes qualitatively different dynamical properties, such as rapid thermalization, trapping in metastable superfluid or normal states, as well as long-lived or strongly damped amplitude oscillations. We summarize our results in nonequilibrium "phase diagrams" that map out the different dynamical regimes.
Mean field limit for bosons and propagation of Wigner measures
Ammari, Z
2008-01-01
We consider the N-body Schr\\"{o}dinger dynamics of bosons in the mean field limit with a bounded pair-interaction potential. According to the previous work \\cite{AmNi}, the mean field limit is translated into a semiclassical problem with a small parameter $\\epsilon\\to 0$, after introducing an $\\epsilon$-dependent bosonic quantization. The limit is 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 in \\cite{AmNi} in the infinite dimensional setting. The additional result presented here states that the transport by the nonlinear flow holds for rather general class of quantum states in their mean field limit.
Regularity Theory for Mean-Field Game Systems
Gomes, Diogo A.
2016-09-14
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.
A mean field theory of coded CDMA systems
Yano, Toru [Graduate School of Science and Technology, Keio University, Hiyoshi, Kohoku-ku, Yokohama-shi, Kanagawa 223-8522 (Japan); Tanaka, Toshiyuki [Graduate School of Informatics, Kyoto University, Yoshida Hon-machi, Sakyo-ku, Kyoto-shi, Kyoto 606-8501 (Japan); Saad, David [Neural Computing Research Group, Aston University, Birmingham B4 7ET (United Kingdom)], E-mail: yano@thx.appi.keio.ac.jp
2008-08-15
We present a mean field theory of code-division multiple-access (CDMA) systems with error-control coding. On the basis of the relation between the free energy and mutual information, we obtain an analytical expression of the maximum spectral efficiency of the coded CDMA system, from which a mean-field description of the coded CDMA system is provided in terms of a bank of scalar Gaussian channels whose variances in general vary at different code symbol positions. Regular low-density parity-check (LDPC)-coded CDMA systems are also discussed as an example of the coded CDMA systems.
Large amplitude motion with a stochastic mean-field approach
Yilmaz Bulent
2012-12-01
Full Text Available In the stochastic mean-field approach, an ensemble of initial conditions is considered to incorporate correlations beyond the mean-field. Then each starting point is propagated separately using the Time-Dependent Hartree-Fock equation of motion. This approach provides a rather simple tool to better describe fluctuations compared to the standard TDHF. Several illustrations are presented showing that this theory can be rather effective to treat the dynamics close to a quantum phase transition. Applications to fusion and transfer reactions demonstrate the great improvement in the description of mass dispersion.
An Adaptive Filtering Algorithm using Mean Field Annealing Techniques
Persson, Per; Nordebo, Sven; Claesson, Ingvar
2002-01-01
We present a new approach to discrete adaptive filtering based on the mean field annealing algorithm. The main idea is to find the discrete filter vector that minimizes the matrix form of the Wiener-Hopf equations in a least-squares sense by a generalized mean field annealing algorithm. It is indicated by simulations that this approach, with complexity O(M^2) where M is the filter length, finds a solution comparable to the one obtained by the recursive least squares (RLS) algorithm but withou...
Socio-economic applications of finite state mean field games
Gomes, Diogo A.
2014-10-06
In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments,which show interesting phenomena such as shock formation. Hence, we conclude with an investigation of the shock structure in the case of two-state problems.
Suppression of oscillations in mean-field diffusion
Neeraj Kumar Kamal; Pooja Rani Sharma; Manish Dev Shrimali
2015-02-01
We study the role of mean-field diffusive coupling on suppression of oscillations for systems of limit cycle oscillators. We show that this coupling scheme not only induces amplitude death (AD) but also oscillation death (OD) in coupled identical systems. The suppression of oscillations in the parameter space crucially depends on the value of mean-field diffusion parameter. It is also found that the transition from oscillatory solutions to OD in conjugate coupling case is different from the case when the coupling is through similar variable. We rationalize our study using linear stability analysis.
Bruce, Adam L
2015-01-01
We show the traditional rocket problem, where the ejecta velocity is assumed constant, can be reduced to an integral quadrature of which the completely non-relativistic equation of Tsiolkovsky, as well as the fully relativistic equation derived by Ackeret, are limiting cases. By expanding this quadrature in series, it is shown explicitly how relativistic corrections to the mass ratio equation as the rocket transitions from the Newtonian to the relativistic regime can be represented as products of exponential functions of the rocket velocity, ejecta velocity, and the speed of light. We find that even low order correction products approximate the traditional relativistic equation to a high accuracy in flight regimes up to $0.5c$ while retaining a clear distinction between the non-relativistic base-case and relativistic corrections. We furthermore use the results developed to consider the case where the rocket is not moving relativistically but the ejecta stream is, and where the ejecta stream is massless.
Noisy mean field game model for malware propagation in opportunistic networks
Tembine, Hamidou
2012-01-01
In this paper we present analytical mean field techniques that can be used to better understand the behavior of malware propagation in opportunistic large networks. We develop a modeling methodology based on stochastic mean field optimal control that is able to capture many aspects of the problem, especially the impact of the control and heterogeneity of the system on the spreading characteristics of malware. The stochastic large process characterizing the evolution of the total number of infected nodes is examined with a noisy mean field limit and compared to a deterministic one. The stochastic nature of the wireless environment make stochastic approaches more realistic for such types of networks. By introducing control strategies, we show that the fraction of infected nodes can be maintained below some threshold. In contrast to most of the existing results on mean field propagation models which focus on deterministic equations, we show that the mean field limit is stochastic if the second moment of the number of object transitions per time slot is unbounded with the size of the system. This allows us to compare one path of the fraction of infected nodes with the stochastic trajectory of its mean field limit. In order to take into account the heterogeneity of opportunistic networks, the analysis is extended to multiple types of nodes. Our numerical results show that the heterogeneity can help to stabilize the system. We verify the results through simulation showing how to obtain useful approximations in the case of very large systems. © 2012 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering.
Mean-field versus microconvection effects in nanofluid thermal conduction.
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.
Two numerical methods for mean-field games
Gomes, Diogo A.
2016-01-09
Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.
Condition monitoring with Mean field independent components analysis
Pontoppidan, Niels Henrik; Sigurdsson, Sigurdur; Larsen, Jan
2005-01-01
We discuss condition monitoring based on mean field independent components analysis of acoustic emission energy signals. Within this framework it is possible to formulate a generative model that explains the sources, their mixing and also the noise statistics of the observed signals. By using...
Mean-Field Versus Microconvection Effects in Nanofluid Thermal Conduction
Eapen, Jacob; Williams, Wesley C.; Buongiorno, Jacopo; Hu, Lin-Wen; Yip, Sidney; Rusconi, Roberto; Piazza, Roberto
2007-08-01
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.
Photoassociation of Atomic BEC within Mean-Field Approximation:Exact Solutions
CAI Wei; JING Hui; ZHAN Ming-Sheng; XU Jing-Jun
2007-01-01
We propose an exactly solvable method to study the coherent two-colour photoassociation of an atomic BoseEinstein condensate,by linearizing the bilinear atom-molecule coupling,which allows su to conveniently probe the quantum dynamics and statistics of the system.By preparing different initial states of the atomic condensate,we can observe very different quantum statistical properties of the system by exactly calculating the quadraturesqueezed and mode-correlated functions.
Adaptive and self-averaging Thouless-Anderson-Palmer mean-field theory for probabilistic modeling
Opper, Manfred; Winther, Ole
2001-01-01
We develop a generalization of the Thouless-Anderson-Palmer (TAP) mean-field approach of disorder physics. which makes the method applicable to the computation of approximate averages in probabilistic models for real data. In contrast to the conventional TAP approach, where the knowledge of the d......We develop a generalization of the Thouless-Anderson-Palmer (TAP) mean-field approach of disorder physics. which makes the method applicable to the computation of approximate averages in probabilistic models for real data. In contrast to the conventional TAP approach, where the knowledge...... distributions in the thermodynamic limit. On the other hand, simulations on a real data model demonstrate that the method achieves more accurate predictions as compared to conventional TAP approaches....
Inverse Magnetic Catalysis in Nambu--Jona-Lasinio Model beyond Mean Field
Mao, Shijun
2016-01-01
We study inverse magnetic catalysis in the Nambu--Jona-Lasinio model beyond mean field approximation. The feed-down from mesons to quarks is embedded in an effective coupling constant at finite temperature and magnetic field. While the magnetic catalysis is still the dominant effect at low temperature, the meson dressed quark mass drops down with increasing magnetic field at high temperature due to the dimension reduction of the Goldstone mode in the Pauli-Villars regularization scheme.
Point-coupling models from mesonic hyper massive limit and mean-field approaches
Lourenco, O.; Dutra, M., E-mail: odilon@ita.br [Departamento de Fisica, Instituto Tecnologico da Aeronautica - CTA, Sao Jose dos Campos, SP (Brazil); Delfino, Antonio, E-mail: delfino@if.uff.br [Instituto de Fisica, Universidade Federal Fluminense, Niteroi, RJ (Brazil); Amaral, R.L.P.G. [Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA (United States)
2012-08-15
t In this work, we show how nonlinear point coupling models, described by a Lagrangian density containing only terms up to fourth order in the fermion condensate ({Psi}-bar{Psi}), are derived from a modified meson exchange nonlinear Walecka model. We present two methods of derivation, namely the hyper massive meson limit within a functional integral approach and the mean-field approximation, in which equations of state at zero temperature of the nonlinear point-coupling models are directly obtained. (author)
Mean field and collisional dynamics of interacting fermion-boson systems the Jaynes-Cummings model
Takano-Natti, E R
1996-01-01
A general time-dependent projection technique is applied to the study of the dynamics of quantum correlations in a system consisting of interacting fermionic and bosonic subsystems, described by the Jaynes-Cummings Hamiltonian. The amplitude modulation of the Rabi oscillations which occur for a strong, coherent initial bosonic field is obtained from the spin intrinsic depolarization resulting from collisional corrections to the mean-field approximation.
Nonlinear Effects in Quantum Dynamics of Atom Laser: Mean-Field Approach
JING Hui
2002-01-01
Quantum dynamics and statistics of an atom laser with nonlinear binary interactions are investigated inthe framework of mean-field approximation. The linearized effective Hamiltonian of the system is accurately solvable.It is shown that, although the input radio frequency field is in an ordinary Glauber coherent state, the output matterwave will periodically exhibit quadrature squeezing effects purely originated from the nonlinear atom-atom collisions.
A mean field theory for the cold quark gluon plasma applied to stellar structure
Fogaca, D. A.; Navarra, F. S.; Franzon, B. [Instituto de Fisica, Universidade de Sao Paulo Rua do Matao, Travessa R, 187, 05508-090 Sao Paulo, SP (Brazil); Horvath, J. E. [Instituto de Astronomia, Geofisica e Ciencias Atmosfericas, Universidade de Sao Paulo, Rua do Matao, 1226, 05508-090, Sao Paulo, SP (Brazil)
2013-03-25
An equation of state based on a mean-field approximation of QCD is used to describe the cold quark gluon plasma and also to study the structure of compact stars. We obtain stellar masses compatible with the pulsar PSR J1614-2230 that was determined to have a mass of (1.97 {+-} 0.04 M{sub Circled-Dot-Operator }), and the corresponding radius around 10-11 km.
A simplified BBGKY hierarchy for correlated fermionic systems from a Stochastic Mean-Field approach
Lacroix, Denis; Ayik, Sakir; Yilmaz, Bulent
2015-01-01
The stochastic mean-field (SMF) approach allows to treat correlations beyond mean-field using a set of independent mean-field trajectories with appropriate choice of fluctuating initial conditions. We show here, that this approach is equivalent to a simplified version of the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy between one-, two-, ..., N-body degrees of freedom. In this simplified version, one-body degrees of freedom are coupled to fluctuations to all orders while retaining only specific terms of the general BBGKY hierarchy. The use of the simplified BBGKY is illustrated with the Lipkin-Meshkov-Glick (LMG) model. We show that a truncated version of this hierarchy can be useful, as an alternative to the SMF, especially in the weak coupling regime to get physical insight in the effect beyond mean-field. In particular, it leads to approximate analytical expressions for the quantum fluctuations both in the weak and strong coupling regime. In the strong coupling regime, it can only be used for sho...
A simplified BBGKY hierarchy for correlated fermions from a stochastic mean-field approach
Lacroix, Denis; Tanimura, Yusuke [Universite Paris-Sud, Institut de Physique Nucleaire, IN2P3-CNRS, Orsay (France); Ayik, Sakir [Tennessee Technological University, Physics Department, Cookeville, TN (United States); Yilmaz, Bulent [Ankara University, Physics Department, Faculty of Sciences, Ankara (Turkey)
2016-04-15
The stochastic mean-field (SMF) approach allows to treat correlations beyond mean-field using a set of independent mean-field trajectories with appropriate choice of fluctuating initial conditions. We show here that this approach is equivalent to a simplified version of the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy between one-, two-,.., N -body degrees of freedom. In this simplified version, one-body degrees of freedom are coupled to fluctuations to all orders while retaining only specific terms of the general BBGKY hierarchy. The use of the simplified BBGKY is illustrated with the Lipkin-Meshkov-Glick (LMG) model. We show that a truncated version of this hierarchy can be useful, as an alternative to the SMF, especially in the weak coupling regime to get physical insight in the effect beyond mean-field. In particular, it leads to approximate analytical expressions for the quantum fluctuations both in the weak and strong coupling regime. In the strong coupling regime, it can only be used for short time evolution. In that case, it gives information on the evolution time-scale close to a saddle point associated to a quantum phase-transition. For long time evolution and strong coupling, we observed that the simplified BBGKY hierarchy cannot be truncated and only the full SMF with initial sampling leads to reasonable results. (orig.)
Chaotic time series prediction using mean-field theory for support vector machine
Cui Wan-Zhao; Zhu Chang-Chun; Bao Wen-Xing; Liu Jun-Hua
2005-01-01
This paper presents a novel method for predicting chaotic time series which is based on the support vector machines approach, and it uses the mean-field theory for developing an easy and efficient learning procedure for the support vector machine. The proposed method approximates the distribution of the support vector machine parameters to a Gaussian process and uses the mean-field theory to estimate these parameters easily, and select the weights of the mixture of kernels used in the support vector machine estimation more accurately and faster than traditional quadratic programming-based algorithms. Finally, relationships between the embedding dimension and the predicting performance of this method are discussed, and the Mackey-Glass equation is applied to test this method. The stimulations show that the mean-field theory for support vector machine can predict chaotic time series accurately, and even if the embedding dimension is unknown, the predicted results are still satisfactory. This result implies that the mean-field theory for support vector machine is a good tool for studying chaotic time series.
Pseudospin symmetry in finite nuclei within the relativistic Hartree-Fock framework
Lopez-Quelle, M [Departamento de Fisica Aplicada, Universidad de Cantabria, E-39005 Santander (Spain); Savushkin, L N [Department of Physics, St Petersburg University for Telecommunications, 191186 St Petersburg (Russian Federation); Marcos, S [Departamento de Fisica Moderna, Universidad de Cantabria, E-39005 Santander (Spain); Niembro, R [Departamento de Fisica Moderna, Universidad de Cantabria, E-39005 Santander (Spain)
2005-10-01
In the present work, we analyse the behaviour of the pseudospin symmetry (PSS) in heavy nuclei ({sup 208}Pb) in the framework of the relativistic Hartree-Fock approximation (RHFA). The quasidegeneracy of the pseudospin partners and the similarity of the small F components of their respective Dirac spinors have a somewhat lower degree of accuracy than in the relativistic mean field approximation (RMFA). Both properties improve when the number of nodes of the small component increases, as happens in the RMFA. The behaviour of the single-particle potentials appearing in the Dirac equation of the pseudospin partners is analysed. There is no dominance of the pseudocentrifugal barrier (PCB) compared to the pseudospin-orbit potential (PSOP). In the RHFA, the PSS is an approximately satisfied symmetry in nuclei and its dynamical character is reinforced with respect to the RMFA.
Hadron resonance gas and mean-field nuclear matter for baryon number fluctuations
Fukushima, Kenji
2014-01-01
We give an estimate for the skewness and the kurtosis of the baryon number distribution in two representative models; i.e., models for a hadron resonance gas and relativistic mean-field nuclear matter. We emphasize formal similarity between these two descriptions. The hadron resonance gas leads to a deviation from the Skellam distribution if quantum statistical correlation is taken into account at high baryon density, but this effect is not strong enough to explain fluctuation data seen in the beam-energy scan at RHIC/STAR. In the calculation of mean-field nuclear matter the density correlation with the vector \\omega-field rather than the effective mass with the scalar \\sigma-field renders the kurtosis suppressed at higher baryon density so as to account for the observed behavior of the kurtosis. We finally discuss the difference between the baryon number and the proton number fluctuations from correlation effects in isospin space. Our numerical results suggest that such effects are only minor even in the cas...
Entanglement spectrum in cluster dynamical mean-field theory
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.
Mean-field theory of echo state networks
Massar, Marc; Massar, Serge
2013-04-01
Dynamical systems driven by strong external signals are ubiquitous in nature and engineering. Here we study “echo state networks,” networks of a large number of randomly connected nodes, which represent a simple model of a neural network, and have important applications in machine learning. We develop a mean-field theory of echo state networks. The dynamics of the network is captured by the evolution law, similar to a logistic map, for a single collective variable. When the network is driven by many independent external signals, this collective variable reaches a steady state. But when the network is driven by a single external signal, the collective variable is non stationary but can be characterized by its time averaged distribution. The predictions of the mean-field theory, including the value of the largest Lyapunov exponent, are compared with the numerical integration of the equations of motion.
Analytic Beyond-Mean-Field BEC Wave Functions
Dunn, Martin; Laing, W. Blake; Watson, Deborah K.; Loeser, John G.
2006-05-01
We present analytic N-body beyond-mean-field wave functions for Bose-Einstein condensates. This extends our previous beyond-mean-field energy calculations to the substantially more difficult problem of determining correlated N-body wave functions for a confined system. The tools used to achieve this have been carefully chosen to maximize the use of symmetry and minimize the dependence on numerical computation. We handle the huge number of interactions when N is large (˜N^2/2 two-body interactions) by bringing together three theoretical methods. These are dimensional perturbation theory, the FG method of Wilson et al, and the group theory of the symmetric group. The wave function is then used to derive the density profile of a condensate in a cylindrical trap.This method makes no assumptions regarding the form or strength of the interactions and is applicable to both small-N and large-N systems.
Characterizing the mean-field dynamo in turbulent accretion disks
Gressel, Oliver
2015-01-01
The formation and evolution of a wide class of astrophysical objects is governed by turbulent, magnetized accretion disks. Understanding their secular dynamics is of primary importance. Apart from enabling mass accretion via the transport of angular momentum, the turbulence affects the long-term evolution of the embedded magnetic flux, which in turn regulates the efficiency of the transport. In this paper, we take a comprehensive next step towards an effective mean-field model for turbulent astrophysical disks by systematically studying the key properties of magnetorotational turbulence in vertically-stratified, isothermal shearing boxes. This allows us to infer emergent properties of the ensuing chaotic flow as a function of the shear parameter as well as the amount of net-vertical flux. Using the test-field method, we furthermore characterize the mean-field dynamo coefficients that describe the long-term evolution of large-scale fields. We simultaneously infer the vertical shape and the spectral scale depen...
Nuclear collective vibrations in extended mean-field theory
Lacroix, D. [Lab. de Physique Corpusculaire/ ENSICAEN, 14 - Caen (France); Ayik, S. [Tennessee Technological Univ., Cookeville, TN (United States); Chomaz, Ph. [Grand Accelerateur National d' Ions Lourds (GANIL), 14 - Caen (France)
2003-07-01
The extended mean-field theory, which includes both the incoherent dissipation mechanism due to nucleon-nucleon collisions and the coherent dissipation mechanism due to coupling to low-lying surface vibrations, is briefly reviewed. Expressions of the strength functions for the collective excitations are presented in the small amplitude limit of this approach. This fully microscopic theory is applied by employing effective Skyrme forces to various giant resonance excitations at zero and finite temperature. The theory is able to describe the gross properties of giant resonance excitations, the fragmentation of the strength distributions as well as their fine structure. At finite temperature, the success and limitations of this extended mean-field description are discussed. (authors)
Schrödinger Approach to Mean Field Games
Swiecicki, Igor; Gobron, Thierry; Ullmo, Denis
2016-03-01
Mean field games (MFG) provide a theoretical frame to model socioeconomic systems. In this Letter, we study a particular class of MFG that shows strong analogies with the nonlinear Schrödinger and Gross-Pitaevskii equations introduced in physics to describe a variety of physical phenomena. Using this bridge, many results and techniques developed along the years in the latter context can be transferred to the former, which provides both a new domain of application for the nonlinear Schrödinger equation and a new and fruitful approach in the study of mean field games. Utilizing this approach, we analyze in detail a population dynamics model in which the "players" are under a strong incentive to coordinate themselves.
Mean-field theory of a recurrent epidemiological model.
Nagy, Viktor
2009-06-01
Our purpose is to provide a mean-field theory for the discrete time-step susceptible-infected-recovered-susceptible (SIRS) model on uncorrelated networks with arbitrary degree distributions. The effect of network structure, time delays, and infection rate on the stability of oscillating and fixed point solutions is examined through analysis of discrete time mean-field equations. Consideration of two scenarios for disease contagion demonstrates that the manner in which contagion is transmitted from an infected individual to a contacted susceptible individual is of primary importance. In particular, the manner of contagion transmission determines how the degree distribution affects model behavior. We find excellent agreement between our theoretical results and numerical simulations on networks with large average connectivity.
Communication patterns in mean field models for wireless sensor networks
2015-01-01
Wireless sensor networks are usually composed of a large number of nodes, and with the increasing processing power and power consumption efficiency they are expected to run more complex protocols in the future. These pose problems in the field of verification and performance evaluation of wireless networks. In this paper, we tailor the mean-field theory as a modeling technique to analyze their behavior. We apply this method to the slotted ALOHA protocol, and establish results on the long term...
Dynamical mean-field theory for flat-band ferromagnetism
Nguyen, Hong-Son; Tran, Minh-Tien
2016-09-01
The magnetically ordered phase in the Hubbard model on the infinite-dimensional hyper-perovskite lattice is investigated within dynamical mean-field theory. It turns out for the infinite-dimensional hyper-perovskite lattice the self-consistent equations of dynamical mean-field theory are exactly solved, and this makes the Hubbard model exactly solvable. We find electron spins are aligned in the ferromagnetic or ferrimagnetic configuration at zero temperature and half filling of the edge-centered sites of the hyper-perovskite lattice. A ferromagnetic-ferrimagnetic phase transition driven by the energy level splitting is found and it occurs through a phase separation. The origin of ferromagnetism and ferrimagnetism arises from the band flatness and the virtual hybridization between macroscopically degenerate flat bands and dispersive ones. Based on the exact solution in the infinite-dimensional limit, a modified exact diagonalization as the impurity solver for dynamical mean-field theory on finite-dimensional perovskite lattices is also proposed and examined.
HBT Pion Interferometry with Phenomenological Mean Field Interaction
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.
Mean field study of a propagation-turnover lattice model for the dynamics of histone marking
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.
Mean-field dynamics of a population of stochastic map neurons
Franović, Igor; Maslennikov, Oleg V.; Bačić, Iva; Nekorkin, Vladimir I.
2017-07-01
We analyze the emergent regimes and the stimulus-response relationship of a population of noisy map neurons by means of a mean-field model, derived within the framework of cumulant approach complemented by the Gaussian closure hypothesis. It is demonstrated that the mean-field model can qualitatively account for stability and bifurcations of the exact system, capturing all the generic forms of collective behavior, including macroscopic excitability, subthreshold oscillations, periodic or chaotic spiking, and chaotic bursting dynamics. Apart from qualitative analogies, we find a substantial quantitative agreement between the exact and the approximate system, as reflected in matching of the parameter domains admitting the different dynamical regimes, as well as the characteristic properties of the associated time series. The effective model is further shown to reproduce with sufficient accuracy the phase response curves of the exact system and the assembly's response to external stimulation of finite amplitude and duration.
State-of-the-art of beyond mean field theories with nuclear density functionals
Egido, J Luis
2016-01-01
We present an overview of beyond mean field theories (BMFT) based on the generator coordinate method (GCM) and the recovery of symmetries used in nuclear physics with effective forces. After a reminder of the Hartree-Fock-Bogoliubov (HFB) theory a discussion of the shortcomings of any mean field approximation (MFA) is presented. The recovery of the symmetries spontaneously broken in the HFB approach, in particular the angular momentum, is necessary, among others, to describe excited states and transitions. Particle number projection is needed to guarantee the right number of protons and neutrons. Furthermore a projection before the variation prevents the pairing collapse in the weak pairing regime. The lack of fluctuations around the average values of the MFA is a shortcoming of this approach. To build in correlations in BMFT one selects the relevant degrees of freedom: quadrupole, octupole and the pairing vibrations as well as the single particle ones. In the GCM the operators representing these degrees of f...
Spectral properties of the one-dimensional Hubbard model: cluster dynamical mean-field approaches
Go, Ara; Jeon, Gun Sang
2011-03-01
We investigate static and dynamic properties of the one-dimensional Hubbard model using cluster extensions of the dynamical mean-field theory. It is shown that the two different extensions, the cellular dynamical mean-field theory and the dynamic cluster approximation, yield the ground-state properties which are qualitatively in good agreement with each other. We compare the results with the Bethe ansatz results to check the accuracy of the calculation with finite sizes of clusters. We also analyze the spectral properties of the model with the focus on the spin-charge separation and discuss the dependency on the cluster size in the two approaches. This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(2010-0010937).
Oscillating epidemics in a dynamic network model: stochastic and mean-field analysis.
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.
Skymapping with OSSE via the Mean Field Annealing Pixon Technique
Dixon, D D; Zych, A D; Cheng, L X; Johnson, W N; Kurfess, J D; Pina, R K; Pütter, R C; Purcell, W R; Wheaton, W A; Wheaton, Wm. A.
1997-01-01
We present progress toward using scanned OSSE observations for mapping and sky survey work. To this end, we have developed a technique for detecting pointlike sources of unknown number and location, given that they appear in a background which is relatively featureless or which can be modeled. The technique, based on the newly developed concept and mean field annealing, is described, with sample reconstructions of data from the OSSE Virgo Survey. The results demonstrate the capability of reconstructing source information without any a priori information about the number and/or location of pointlike sources in the field-of-view.
Small-world network spectra in mean-field theory.
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.
Time-Dependent Mean-Field Games with Logarithmic Nonlinearities
Gomes, Diogo A.
2015-10-06
In this paper, we prove the existence of classical solutions for time-dependent mean-field games with a logarithmic nonlinearity and subquadratic Hamiltonians. Because the logarithm is unbounded from below, this nonlinearity poses substantial mathematical challenges that have not been addressed in the literature. Our result is proven by recurring to a delicate argument which combines Lipschitz regularity for the Hamilton-Jacobi equation with estimates for the nonlinearity in suitable Lebesgue spaces. Lipschitz estimates follow from an application of the nonlinear adjoint method. These are then combined with a priori bounds for solutions of the Fokker-Planck equation and a concavity argument for the nonlinearity.
A mean-field game economic growth model
Gomes, Diogo A.
2016-08-05
Here, we examine a mean-field game (MFG) that models the economic growth of a population of non-cooperative, rational agents. In this MFG, agents are described by two state variables - the capital and consumer goods they own. Each agent seeks to maximize his/her utility by taking into account statistical data about the whole population. The individual actions drive the evolution of the players, and a market-clearing condition determines the relative price of capital and consumer goods. We study the existence and uniqueness of optimal strategies of the agents and develop numerical methods to compute these strategies and the equilibrium price.
Mean-field theory and self-consistent dynamo modeling
Yoshizawa, Akira; Yokoi, Nobumitsu [Tokyo Univ. (Japan). Inst. of Industrial Science; Itoh, Sanae-I [Kyushu Univ., Fukuoka (Japan). Research Inst. for Applied Mechanics; Itoh, Kimitaka [National Inst. for Fusion Science, Toki, Gifu (Japan)
2001-12-01
Mean-field theory of dynamo is discussed with emphasis on the statistical formulation of turbulence effects on the magnetohydrodynamic equations and the construction of a self-consistent dynamo model. The dynamo mechanism is sought in the combination of the turbulent residual-helicity and cross-helicity effects. On the basis of this mechanism, discussions are made on the generation of planetary magnetic fields such as geomagnetic field and sunspots and on the occurrence of flow by magnetic fields in planetary and fusion phenomena. (author)
Asymptotics of Mean-Field O( N) Models
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.
Asymptotics of the mean-field Heisenberg model
Kirkpatrick, Kay
2012-01-01
We consider the mean-field classical Heisenberg model and obtain detailed information about the magnetization by studying the model on a complete graph and sending the number of vertices to infinity. In particular, we obtain Cram\\`er- and Sanov-type large deviations principles for the magnetization and the empirical spin distribution and demonstrate a second-order phase transition in the Gibbs measures. We also study the asymptotics of the magnetization throughout the phase transition using Stein's method, proving central limit theorems in the sub- and supercritical phases and a nonnormal limit theorem at the critical temperature.
A mechanical approach to mean field spin models
Genovese, Giuseppe
2008-01-01
Inspired by the bridge pioneered by Guerra among statistical mechanics on lattice and analytical mechanics on 1+1 continuous Euclidean space-time, we built a self-consistent method to solve for the thermodynamics of mean-field models defined on lattice, whose order parameters self average. We show the whole procedure by analyzing in full details the simplest test case, namely the Curie-Weiss model. Further we report some applications also to models whose order parameters do not self-average, by using the Sherrington-Kirkpatrick spin glass as a guide.
Angular momentum projection for a Nilsson mean-field plus pairing model
Wang, Yin; Pan, Feng; Launey, Kristina D.; Luo, Yan-An; Draayer, J. P.
2016-06-01
The angular momentum projection for the axially deformed Nilsson mean-field plus a modified standard pairing (MSP) or the nearest-level pairing (NLP) model is proposed. Both the exact projection, in which all intrinsic states are taken into consideration, and the approximate projection, in which only intrinsic states with K = 0 are taken in the projection, are considered. The analysis shows that the approximate projection with only K = 0 intrinsic states seems reasonable, of which the configuration subspace considered is greatly reduced. As simple examples for the model application, low-lying spectra and electromagnetic properties of 18O and 18Ne are described by using both the exact and approximate angular momentum projection of the MSP or the NLP, while those of 20Ne and 24Mg are described by using the approximate angular momentum projection of the MSP or NLP.
Mean field theory for U(n) dynamical groups
Rosensteel, G, E-mail: george.rosensteel@tulane.edu [Department of Physics, Tulane University, New Orleans, LA 70118 (United States)
2011-04-22
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 su(2) model and the Elliott su(3) model. When the energy in the su(3) theory is a rotational scalar function, Marsden-Weinstein reduction simplifies AMFT dynamics to a two-dimensional phase space.
Simulated Tempering and Swapping on Mean-Field Models
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.
Non-local correlations within dynamical mean field theory
Li, Gang
2009-03-15
The contributions from the non-local fluctuations to the dynamical mean field theory (DMFT) were studied using the recently proposed dual fermion approach. Straight forward cluster extensions of DMFT need the solution of a small cluster, where all the short-range correlations are fully taken into account. All the correlations beyond the cluster scope are treated in the mean-field level. In the dual fermion method, only a single impurity problem needs to be solved. Both the short and long-range correlations could be considered on equal footing in this method. The weak-coupling nature of the dual fermion ensures the validity of the finite order diagram expansion. The one and two particle Green's functions calculated from the dual fermion approach agree well with the Quantum Monte Carlo solutions, and the computation time is considerably less than with the latter method. The access of the long-range order allows us to investigate the collective behavior of the electron system, e.g. spin wave excitations. (orig.)
Nonlinear regimes in mean-field full-sphere dynamo
Pipin, V V
2016-01-01
The mean-field dynamo model is employed to study the non-linear dynamo regimes in a fully convective star of mass 0.3$M_{\\odot}$ rotating with period of 10 days. The differential rotation law was estimated using the mean-field hydrodynamic and heat transport equations. For the intermediate parameter of the turbulent magnetic Reynolds number, $Pm_{T}=3$ we found the oscillating dynamo regimes with period about 40Yr. The higher $Pm_{T}$ results to longer dynamo periods. The meridional circulation has one cell per hemisphere. It is counter-clockwise in the Northen hemisphere. The amplitude of the flow at the surface around 1 m/s. Tne models with regards for meridional circulation show the anti-symmetric relative to equator magnetic field. If the large-scale flows is fixed we find that the dynamo transits from axisymmetric to non-axisymmetric regimes for the overcritical parameter of the $\\alpha$effect. The change of dynamo regime occurs because of the non-axisymmetric non-linear $\\alpha$-effect. The situation pe...
Kinetic and mean field description of Gibrat's law
Toscani, Giuseppe
2016-01-01
We introduce and analyze a linear kinetic model that describes the evolution of the probability density of the number of firms in a society, in which the microscopic rate of change obeys to the so-called law of proportional effect proposed by Gibrat. Despite its apparent simplicity, the possible mean field limits of the kinetic model are varied. In some cases, the asymptotic limit can be described by a first-order partial differential equation. In other cases, the mean field equation is a linear diffusion with a non constant diffusion coefficient that models also the geometric Brownian motion and can be studied analytically. In this case, it is shown that the large-time behavior of the solution is represented, for a large class of initial data, by a lognormal distribution with constant mean value and variance increasing exponentially in time at a precise rate. The relationship between the kinetic and the diffusion models allow to introduce an easy-to- implement expression for computing the Fourier transform o...
The effectiveness of mean-field theory for avalanche distributions
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.
Kinetic and mean field description of Gibrat's law
Toscani, Giuseppe
2016-11-01
I introduce and analyze a linear kinetic model that describes the evolution of the probability density of the number of firms in a society, in which the microscopic rate of change obeys to the so-called law of proportional effect proposed by Gibrat (1930, 1931). Despite its apparent simplicity, the possible mean field limits of the kinetic model are varied. In some cases, the asymptotic limit can be described by a first-order partial differential equation. In other cases, the mean field equation is a linear diffusion with a non constant diffusion coefficient that can be studied analytically, by virtue of a transformation of variables recently utilized in Iagar and Sánchez (2013) to study the heat equation in a nonhomogeneous medium with critical density. In this case, it is shown that the large-time behavior of the solution is represented, for a large class of initial data, by a lognormal distribution with constant mean value and variance increasing exponentially in time at a precise rate.
Demianski, Marek
2013-01-01
Relativistic Astrophysics brings together important astronomical discoveries and the significant achievements, as well as the difficulties in the field of relativistic astrophysics. This book is divided into 10 chapters that tackle some aspects of the field, including the gravitational field, stellar equilibrium, black holes, and cosmology. The opening chapters introduce the theories to delineate gravitational field and the elements of relativistic thermodynamics and hydrodynamics. The succeeding chapters deal with the gravitational fields in matter; stellar equilibrium and general relativity
RELATIVISTIC CALCULATIONS OF THE SUPERHEAVY NUCLEUS 114-298
BOERSMA, HF
1993-01-01
We investigate ground-state properties of the superheavy nucleus with N = 184 and Z = 114, (298)114, using conventional relativistic mean-field theory and density-dependent mean-field theory, which reproduces Dirac-Brueckner calculations in nuclear matter. Our calculations provide support for N = 18
WU Ying; YANG Xiao-Xue
2002-01-01
We present the analytical solutions to the two-mode mean-field model for a split Bose Einstein condensate.These explicit solutions completely determine the system's dynamics under the two-mode mean-field approximation for all possible initial conditions.
Mean Field Limit of Interacting Filaments and Vector Valued Non-linear PDEs
Bessaih, Hakima; Coghi, Michele; Flandoli, Franco
2017-03-01
Families of N interacting curves are considered, with long range, mean field type, interaction. They generalize models based on classical interacting point particles to models based on curves. In this new set-up, a mean field result is proven, as N→ ∞. The limit PDE is vector valued and, in the limit, each curve interacts with a mean field solution of the PDE. This target is reached by a careful formulation of curves and weak solutions of the PDE which makes use of 1-currents and their topologies. The main results are based on the analysis of a nonlinear Lagrangian-type flow equation. Most of the results are deterministic; as a by-product, when the initial conditions are given by families of independent random curves, we prove a propagation of chaos result. The results are local in time for general interaction kernel, global in time under some additional restriction. Our main motivation is the approximation of 3D-inviscid flow dynamics by the interacting dynamics of a large number of vortex filaments, as observed in certain turbulent fluids; in this respect, the present paper is restricted to smoothed interaction kernels, instead of the true Biot-Savart kernel.
Hydrodynamic mean-field solutions of 1D exclusion processes with spatially varying hopping rates
Lakatos, Greg; O'Brien, John; Chou, Tom
2006-03-01
We analyse the open boundary partially asymmetric exclusion process with smoothly varying internal hopping rates in the infinite-size, mean-field limit. The mean-field equations for particle densities are written in terms of Ricatti equations with the steady-state current J as a parameter. These equations are solved both analytically and numerically. Upon imposing the boundary conditions set by the injection and extraction rates, the currents J are found self-consistently. We find a number of cases where analytic solutions can be found exactly or approximated. Results for J from asymptotic analyses for slowly varying hopping rates agree extremely well with those from extensive Monte Carlo simulations, suggesting that mean-field currents asymptotically approach the exact currents in the hydrodynamic limit, as the hopping rates vary slowly over the lattice. If the forward hopping rate is greater than or less than the backward hopping rate throughout the entire chain, the three standard steady-state phases are preserved. Our analysis reveals the sensitivity of the current to the relative phase between the forward and backward hopping rate functions.
Rios, Arnau; Buchler, Mark; Danielewicz, Pawel
2010-01-01
Nonequilibrium Green's function methods allow for an intrinsically consistent description of the evolution of quantal many-body body systems, with inclusion of different types of correlations. In this paper, we focus on the practical developments needed to build a Green's function methodology for nuclear reactions. We start out by considering symmetric collisions of slabs in one dimension within the mean-field approximation. We concentrate on two issues of importance for actual reaction simulations. First, the preparation of the initial state within the same methodology as for the reaction dynamics is demonstrated by an adiabatic switching on of the mean-field interaction, which leads to the mean-field ground state. Second, the importance of the Green's function matrix-elements far away from the spatial diagonal is analyzed by a suitable suppression process that does not significantly affect the evolution of the elements close to the diagonal. The relative lack of importance of the far-away elements is tied t...
Hydrodynamic mean-field solutions of 1D exclusion processes with spatially varying hopping rates
Lakatos, Greg; O' Brien, John; Chou, Tom [Department of Biomathematics and Institute for Pure and Applied Mathematics, UCLA, Los Angeles, CA 90095 (United States)
2006-03-10
We analyse the open boundary partially asymmetric exclusion process with smoothly varying internal hopping rates in the infinite-size, mean-field limit. The mean-field equations for particle densities are written in terms of Ricatti equations with the steady-state current J as a parameter. These equations are solved both analytically and numerically. Upon imposing the boundary conditions set by the injection and extraction rates, the currents J are found self-consistently. We find a number of cases where analytic solutions can be found exactly or approximated. Results for J from asymptotic analyses for slowly varying hopping rates agree extremely well with those from extensive Monte Carlo simulations, suggesting that mean-field currents asymptotically approach the exact currents in the hydrodynamic limit, as the hopping rates vary slowly over the lattice. If the forward hopping rate is greater than or less than the backward hopping rate throughout the entire chain, the three standard steady-state phases are preserved. Our analysis reveals the sensitivity of the current to the relative phase between the forward and backward hopping rate functions.
Graber, P. Jameson, E-mail: jameson-graber@baylor.edu [Baylor University, Department of Mathematics (United States)
2016-12-15
We study a general linear quadratic mean field type control problem and connect it to mean field games of a similar type. The solution is given both in terms of a forward/backward system of stochastic differential equations and by a pair of Riccati equations. In certain cases, the solution to the mean field type control is also the equilibrium strategy for a class of mean field games. We use this fact to study an economic model of production of exhaustible resources.
How to do mean field theory in Feynman gauge and doing it for U(1) with corrections to fourth order
Flyvbjerg, H.
1984-07-02
It is demonstrated how mean field theory with corrections from fluctuations may be applied to lattice gauge theories in covariant gauges. By fixing the gauge at tree level, the importance of fluctuations is decreased. This is understood as inclusion of terms of next-to-leading-order in d in the definition of the mean field tree approximation, d being the dimension of the lattice. The gauge group U(1) and Wilson's action are used as testing ground. Tree and one-loop results comparable to those previously obtained in axial gauge are obtained in for d=4. The next three correction terms to the free and plaquette energies are evaluated in Feynmann gauge. The truncated asympotic series thus obtained is compared to that of the ordinary weak coupling expansion. The mean field series gives, to those orders studied, a much better approximation. The location of phase transitions in 4d and 5d are predicted with 1% error bars.
Neural Population Dynamics Modeled by Mean-Field Graphs
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.
Spectral Synthesis via Mean Field approach Independent Component Analysis
Hu, Ning; Kong, Xu
2015-01-01
In this paper, we apply a new statistical analysis technique, Mean Field approach to Bayesian Independent Component Analysis (MF-ICA), on galaxy spectral analysis. This algorithm can compress the stellar spectral library into a few Independent Components (ICs), and galaxy spectrum can be reconstructed by these ICs. Comparing to other algorithms which decompose a galaxy spectrum into a combination of several simple stellar populations, MF-ICA approach offers a large improvement in the efficiency. To check the reliability of this spectral analysis method, three different methods are used: (1) parameter-recover for simulated galaxies, (2) comparison with parameters estimated by other methods, and (3) consistency test of parameters from the Sloan Digital Sky Survey galaxies. We find that our MF-ICA method not only can fit the observed galaxy spectra efficiently, but also can recover the physical parameters of galaxies accurately. We also apply our spectral analysis method to the DEEP2 spectroscopic data, and find...
Non-mean-field screening by multivalent counterions
Loth, M S; Shklovskii, B I, E-mail: loth@physics.umn.ed [Department of Physics, University of Minnesota, Minneapolis, MN 55455 (United States)
2009-10-21
Screening of a strongly charged macroion by its multivalent counterions cannot be described in the framework of a mean-field Poisson-Boltzmann (PB) theory because multivalent counterions form a strongly correlated liquid (SCL) on the surface of the macroion. It was predicted that a distant counterion polarizes the SCL as if it were a metallic surface and creates an electrostatic image. The attractive potential energy of the image is the reason why the charge density of counterions decreases faster with distance from the charged surface than in PB theory. Using the Monte Carlo method to find the equilibrium distribution of counterions around the macroion, we confirm the existence of the image potential energy. It is also shown that, due to the negative screening length of the SCL, -2xi, the effective metallic surface is actually above the SCL by |xi|.
Explicit Solutions for One-Dimensional Mean-Field Games
Prazeres, Mariana
2017-04-05
In this thesis, we consider stationary one-dimensional mean-field games (MFGs) with or without congestion. Our aim is to understand the qualitative features of these games through the analysis of explicit solutions. We are particularly interested in MFGs with a nonmonotonic behavior, which corresponds to situations where agents tend to aggregate. First, we derive the MFG equations from control theory. Then, we compute explicit solutions using the current formulation and examine their behavior. Finally, we represent the solutions and analyze the results. This thesis main contributions are the following: First, we develop the current method to solve MFG explicitly. Second, we analyze in detail non-monotonic MFGs and discover new phenomena: non-uniqueness, discontinuous solutions, empty regions and unhappiness traps. Finally, we address several regularization procedures and examine the stability of MFGs.
Mean field games with nonlinear mobilities in pedestrian dynamics
Burger, Martin
2014-04-01
In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position, velocity, exit time and the overall density of people. This microscopic setup leads in the mean-field limit to a parabolic optimal control problem. We discuss the modeling of the macroscopic optimal control approach and show how the optimal conditions relate to the Hughes model for pedestrian flow. Furthermore we provide results on the existence and uniqueness of minimizers and illustrate the behavior of the model with various numerical results.
Nuclear Level Density: Shell Model vs Mean Field
Sen'kov, Roman
2015-01-01
The knowledge of the nuclear level density is necessary for understanding various reactions including those in the stellar environment. Usually the combinatorics of Fermi-gas plus pairing is used for finding the level density. Recently a practical algorithm avoiding diagonalization of huge matrices was developed for calculating the density of many-body nuclear energy levels with certain quantum numbers for a full shell-model Hamiltonian. The underlying physics is that of quantum chaos and intrinsic thermalization in a closed system of interacting particles. We briefly explain this algorithm and, when possible, demonstrate the agreement of the results with those derived from exact diagonalization. The resulting level density is much smoother than that coming from the conventional mean-field combinatorics. We study the role of various components of residual interactions in the process of thermalization, stressing the influence of incoherent collision-like processes. The shell-model results for the traditionally...
Metabifurcation analysis of a mean field model of the cortex
Frascoli, Federico; Bojak, Ingo; Liley, David T J
2010-01-01
Mean field models (MFMs) of cortical tissue incorporate salient features of neural masses to model activity at the population level. One of the common aspects of MFM descriptions is the presence of a high dimensional parameter space capturing neurobiological attributes relevant to brain dynamics. We study the physiological parameter space of a MFM of electrocortical activity and discover robust correlations between physiological attributes of the model cortex and its dynamical features. These correlations are revealed by the study of bifurcation plots, which show that the model responses to changes in inhibition belong to two families. After investigating and characterizing these, we discuss their essential differences in terms of four important aspects: power responses with respect to the modeled action of anesthetics, reaction to exogenous stimuli, distribution of model parameters and oscillatory repertoires when inhibition is enhanced. Furthermore, while the complexity of sustained periodic orbits differs ...
Double binding energy differences: Mean-field or pairing effect?
Qi, Chong
2012-10-01
In this Letter we present a systematic analysis on the average interaction between the last protons and neutrons in atomic nuclei, which can be extracted from the double differences of nuclear binding energies. The empirical average proton-neutron interaction Vpn thus derived from experimental data can be described in a very simple form as the interplay of the nuclear mean field and the pairing interaction. It is found that the smooth behavior as well as the local fluctuations of the Vpn in even-even nuclei with N ≠ Z are dominated by the contribution from the proton-neutron monopole interactions. A strong additional contribution from the isoscalar monopole interaction and isovector proton-neutron pairing interaction is seen in the Vpn for even-even N = Z nuclei and for the adjacent odd-A nuclei with one neutron or proton being subtracted.
Mean-field games with logistic population dynamics
Gomes, Diogo A.
2013-12-01
In its standard form, a mean-field game can be defined by coupled system of equations, a Hamilton-Jacobi equation for the value function of agents and a Fokker-Planck equation for the density of agents. Traditionally, the latter equation is adjoint to the linearization of the former. Since the Fokker-Planck equation models a population dynamic, we introduce natural features such as seeding and birth, and nonlinear death rates. In this paper we analyze a stationary meanfield game in one dimension, illustrating various techniques to obtain regularity of solutions in this class of systems. In particular we consider a logistic-type model for birth and death of the agents which is natural in problems where crowding affects the death rate of the agents. The introduction of these new terms requires a number of new ideas to obtain wellposedness. In a forthcoming publication we will address higher dimensional models. ©2013 IEEE.
Glauber Dynamics for the mean-field Potts Model
Cuff, Paul; Louidor, Oren; Lubetzky, Eyal; Peres, Yuval; Sly, Allan
2012-01-01
We study Glauber dynamics for the mean-field (Curie-Weiss) Potts model with $q\\geq 3$ states and show that it undergoes a critical slowdown at an inverse-temperature $\\beta_s(q)$ strictly lower than the critical $\\beta_c(q)$ for uniqueness of the thermodynamic limit. The dynamical critical $\\beta_s(q)$ is the spinodal point marking the onset of metastability. We prove that when $\\beta\\beta_s(q)$ the mixing time is exponentially large in $n$. Furthermore, as $\\beta \\uparrow \\beta_s$ with $n$, the mixing time interpolates smoothly from subcritical to critical behavior, with the latter reached at a scaling window of $O(n^{-2/3})$ around $\\beta_s$. These results form the first complete analysis of the critical slowdown of a dynamics with a first order phase transition.
Glauber Dynamics for the Mean-Field Potts Model
Cuff, P.; Ding, J.; Louidor, O.; Lubetzky, E.; Peres, Y.; Sly, A.
2012-11-01
We study Glauber dynamics for the mean-field (Curie-Weiss) Potts model with q≥3 states and show that it undergoes a critical slowdown at an inverse-temperature β s ( q) strictly lower than the critical β c ( q) for uniqueness of the thermodynamic limit. The dynamical critical β s ( q) is the spinodal point marking the onset of metastability. We prove that when β β s ( q) the mixing time is exponentially large in n. Furthermore, as β↑ β s with n, the mixing time interpolates smoothly from subcritical to critical behavior, with the latter reached at a scaling window of O( n -2/3) around β s . These results form the first complete analysis of mixing around the critical dynamical temperature—including the critical power law—for a model with a first order phase transition.
Quasi-isotropic cascade in MHD turbulence with mean field
Grappin, Roland; Gürcan, Özgür
2012-01-01
We propose a phenomenological theory of incompressible magnetohydrodynamic turbulence in the presence of a strong large-scale magnetic field, which establishes a link between the known anisotropic models of strong and weak MHD turbulence We argue that the Iroshnikov-Kraichnan isotropic cascade develops naturally within the plane perpendicular to the mean field, while oblique-parallel cascades with weaker amplitudes can develop, triggered by the perpendicular cascade, with a reduced flux resulting from a quasi-resonance condition. The resulting energy spectrum $E(k_\\parallel,k_\\bot)$ has the same slope in all directions. The ratio between the extents of the inertial range in the parallel and perpendicular directions is equal to $b_{rms}/B_0$. These properties match those found in recent 3D MHD simulations with isotropic forcing reported in [R. Grappin and W.-C. M\\"uller, Phys. Rev. E \\textbf{82}, 26406 (2010)].
Mean field theory for U(n) dynamical groups
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.
Dynamical Mean-Field Theory and Its Applications to Real Materials
Vollhardt, D.; Held, K.; Keller, G.; Bulla, R.; Pruschke, Th.; Nekrasov, I. A.; Anisimov, V. I.
2005-01-01
Dynamical mean-field theory (DMFT) is a non-perturbative technique for the investigation of correlated electron systems. Its combination with the local density approximation (LDA) has recently led to a material-specific computational scheme for the ab initio investigation of correlated electron materials. The set-up of this approach and its application to materials such as (Sr,Ca)VO3, V2O3, and Cerium is discussed. The calculated spectra are compared with the spectroscopically measured electronic excitation spectra. The surprising similarity between the spectra of the single-impurity Anderson model and of correlated bulk materials is also addressed.
Second-order corrections to mean-field evolution of weakly interacting Bosons, II
Grillakis, M; Margetis, D
2010-01-01
We study the evolution of a N-body weakly interacting system of Bosons. Our work forms an extension of our previous paper I, in which we derived a second-order correction to a mean-field evolution law for coherent states in the presence of small interaction potential. Here, we remove the assumption of smallness of the interaction potential and prove global existence of solutions to the equation for the second-order correction. This implies an improved Fock-space estimate for our approximation of the N-body state.
Delfino, A; Frederico, T
1996-01-01
The link between non-linear chiral effective Lagrangians and the Walecka model description of bulk nuclear matter [1] is questioned. This fact is by itself due to the Mean Field Approximation (MFA) which in nuclear mater makes the picture of a nucleon-nucleon interaction based on scalar(vector) meson exchange, equivalent to the description of a nuclear matter based on attractive and repulsive contact interactions. We present a linear chiral model where this link between the Walecka model and an underlying to chiral symmetry realization still holds, due to MFA.
Mean-Field Semantics for a Process Calculus for Spatially-Explicit Ecological Models
Mauricio Toro
2016-03-01
Full Text Available We define a mean-field semantics for S-PALPS, a process calculus for spatially-explicit, individual-based modeling of ecological systems. The new semantics of S-PALPS allows an interpretation of the average behavior of a system as a set of recurrence equations. Recurrence equations are a useful approximation when dealing with a large number of individuals, as it is the case in epidemiological studies. As a case study, we compute a set of recurrence equations capturing the dynamics of an individual-based model of the transmission of dengue in Bello (Antioquia, Colombia.
舒崧; 李家荣
2012-01-01
We used the Cornwall, Jackiw and Tomboulis （CJT） resummation scheme to study nuclear matter. In the CJT formalism the meson propagators are treated as the bare propagators and the the higher order loop corrections of the thermodynamic potential are evaluated at the Hartree approximation, while the vacuum fluctuations are ignored. Under these treatments in the CJT formalism we derived exact mean-field theory （MFT） results for the nuclear matter. The results are thermodynamically consistent, and our study indicates that the MFT result is the lowest order resummation result in the CJT resummation scheme. The relation between CJT formalism and MFT is clearly presented through the calculations.
Low Complexity Sparse Bayesian Learning for Channel Estimation Using Generalized Mean Field
Pedersen, Niels Lovmand; Manchón, Carles Navarro; Fleury, Bernard Henri
2014-01-01
constrain the auxiliary function approximating the posterior probability density function of the unknown variables to factorize over disjoint groups of contiguous entries in the sparse vector - the size of these groups dictates the degree of complexity reduction. The original high-complexity algorithms......We derive low complexity versions of a wide range of algorithms for sparse Bayesian learning (SBL) in underdetermined linear systems. The proposed algorithms are obtained by applying the generalized mean field (GMF) inference framework to a generic SBL probabilistic model. In the GMF framework, we...
Vrettas, Michail D; Opper, Manfred; Cornford, Dan
2015-01-01
This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over time, dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden Markov models. The algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well-known inference methodologies.
Deterministic Methods for Filtering, part I: Mean-field Ensemble Kalman Filtering
Law, Kody J H; Tempone, Raul
2014-01-01
This paper provides a proof of convergence of the standard EnKF generalized to non-Gaussian state space models, based on the indistinguishability property of the joint distribution on the ensemble. A density-based deterministic approximation of the mean-field EnKF (MFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence k between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for d<2k. The fidelity of approximation of the true distribution is also established using an extension of total variation metric to random measures. This is limited by a Gaussian bias term arising from non-linearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
Chen, Xuwen
2010-01-01
In this paper, we consider the Hamiltonian evolution of N weakly interacting Bosons. Assuming triple collisions with singular potentials, its mean field approximation is given by a quintic Hartree equation. We construct a second order correction to the mean field approximation using a kernel k(t,x,y) and derive an evolution equation for k. We show the global existence for the resulting evolution equation for the correction and establish an apriori estimate comparing the approximation to the exact Hamiltonian evolution. Our error estimate is global and uniform in time. Comparing with the work in [20,11,12] where the error estimate grows in time, our approximation tracks the exact dynamics for all time with an error of the order O(1/$\\sqrt{N}$).
The quark mean field model with pion and gluon corrections
Xing, Xueyong; Shen, Hong
2016-01-01
The properties of nuclear matter and finite nuclei are studied within the quark mean field (QMF) model by taking the effects of pion and gluon into account at the quark level. The nucleon is described as the combination of three constituent quarks confined by a harmonic oscillator potential. To satisfy the spirit of QCD theory, the contributions of pion and gluon on the nucleon structure are treated in second-order perturbation theory. For the nuclear many-body system, nucleons interact with each other by exchanging mesons between quarks. With different constituent quark mass, $m_q$, we determine three parameter sets about the coupling constants between mesons and quarks, named as QMF-NK1, QMF-NK2, and QMF-NK3 by fitting the ground-state properties of several closed-shell nuclei. It is found that all of the three parameter sets can give satisfactory description on properties of nuclear matter and finite nuclei, meanwhile they can also predict the larger neutron star mass around $2.3M_\\odot$ without the hypero...
Quark mean field model with pion and gluon corrections
Xing, Xueyong; Hu, Jinniu; Shen, Hong
2016-10-01
The properties of nuclear matter and finite nuclei are studied within the quark mean field (QMF) model by taking the effects of pions and gluons into account at the quark level. The nucleon is described as the combination of three constituent quarks confined by a harmonic oscillator potential. To satisfy the spirit of QCD theory, the contributions of pions and gluons on the nucleon structure are treated in second-order perturbation theory. In a nuclear many-body system, nucleons interact with each other by exchanging mesons between quarks. With different constituent quark mass, mq, we determine three parameter sets for the coupling constants between mesons and quarks, named QMF-NK1, QMF-NK2, and QMF-NK3, by fitting the ground-state properties of several closed-shell nuclei. It is found that all of the three parameter sets can give a satisfactory description of properties of nuclear matter and finite nuclei, moreover they also predict a larger neutron star mass around 2.3 M⊙ without hyperon degrees of freedom.
One-Dimensional Forward–Forward Mean-Field Games
Gomes, Diogo A.
2016-11-01
While the general theory for the terminal-initial value problem for mean-field games (MFGs) has achieved a substantial progress, the corresponding forward–forward problem is still poorly understood—even in the one-dimensional setting. Here, we consider one-dimensional forward–forward MFGs, study the existence of solutions and their long-time convergence. First, we discuss the relation between these models and systems of conservation laws. In particular, we identify new conserved quantities and study some qualitative properties of these systems. Next, we introduce a class of wave-like equations that are equivalent to forward–forward MFGs, and we derive a novel formulation as a system of conservation laws. For first-order logarithmic forward–forward MFG, we establish the existence of a global solution. Then, we consider a class of explicit solutions and show the existence of shocks. Finally, we examine parabolic forward–forward MFGs and establish the long-time convergence of the solutions.
A Mean-Field Theory for Coarsening Faceted Surfaces
Norris, Scott A
2009-01-01
A mean-field theory is developed for the scale-invariant length distributions observed during the coarsening of one-dimensional faceted surfaces. This theory closely follows the Lifshitz-Slyozov-Wagner theory of Ostwald ripening in two-phase systems [1-3], but the mechanism of coarsening in faceted surfaces requires the addition of convolution terms recalling the work of Smoluchowski [4] and Schumann [5] on coalescence. The model is solved by the exponential distribution, but agreement with experiment is limited by the assumption that neighboring facet lengths are uncorrelated. However, the method concisely describes the essential processes operating in the scaling state, illuminates a clear path for future refinement, and offers a framework for the investigation of faceted surfaces evolving under arbitrary dynamics. [1] I. Lifshitz, V. Slezov, Soviet Physics JETP 38 (1959) 331-339. [2] I. Lifshitz, V. Slyozov, J. Phys. Chem. Solids 19 (1961) 35-50. [3] C. Wagner, Elektrochemie 65 (1961) 581-591. [4] M. von S...
Spectral Synthesis via Mean Field approach to Independent Component Analysis
Hu, Ning; Su, Shan-Shan; Kong, Xu
2016-03-01
We apply a new statistical analysis technique, the Mean Field approach to Independent Component Analysis (MF-ICA) in a Bayseian framework, to galaxy spectral analysis. This algorithm can compress a stellar spectral library into a few Independent Components (ICs), and the galaxy spectrum can be reconstructed by these ICs. Compared to other algorithms which decompose a galaxy spectrum into a combination of several simple stellar populations, the MF-ICA approach offers a large improvement in efficiency. To check the reliability of this spectral analysis method, three different methods are used: (1) parameter recovery for simulated galaxies, (2) comparison with parameters estimated by other methods, and (3) consistency test of parameters derived with galaxies from the Sloan Digital Sky Survey. We find that our MF-ICA method can not only fit the observed galaxy spectra efficiently, but can also accurately recover the physical parameters of galaxies. We also apply our spectral analysis method to the DEEP2 spectroscopic data, and find it can provide excellent fitting results for low signal-to-noise spectra.
Metastability for the Exclusion Process with Mean-Field Interaction
Asselah, Amine; Giacomin, Giambattista
1998-12-01
We consider an exclusion particle system with long-range, mean-field-type interactions at temperature 1/β. The hydrodynamic limit of such a system is given by an integrodifferential equation with one conservation law on the circle C: it is the gradient flux of the Kac free energy functional F β. For β≤1, any constant function with value m ∈ [-1, +1] is the global minimizer of F β in the space \\{ u:int_C {u(x)} dx = m\\} . For β>1, F β restricted to \\{ u:int_C {u(x)} dx = m\\} may have several local minima: in particular, the constant solution may not be the absolute minimizer of F β. We therefore study the long-time behavior of the particle system when the initial condition is close to a homogeneous stable state, giving results on the time of exit from (suitable) subsets of its domain of attraction. We follow the Freidlin-Wentzell approach: first, we study in detail F β together with the time asymptotics of the solution of the hydrodynamic equation; then we study the probability of rare events for the particle system, i.e., large deviations from the hydrodynamic limit.
One-Dimensional Forward–Forward Mean-Field Games
Gomes, Diogo A., E-mail: diogo.gomes@kaust.edu.sa; Nurbekyan, Levon; Sedjro, Marc [King Abdullah University of Science and Technology (KAUST), CEMSE Division (Saudi Arabia)
2016-12-15
While the general theory for the terminal-initial value problem for mean-field games (MFGs) has achieved a substantial progress, the corresponding forward–forward problem is still poorly understood—even in the one-dimensional setting. Here, we consider one-dimensional forward–forward MFGs, study the existence of solutions and their long-time convergence. First, we discuss the relation between these models and systems of conservation laws. In particular, we identify new conserved quantities and study some qualitative properties of these systems. Next, we introduce a class of wave-like equations that are equivalent to forward–forward MFGs, and we derive a novel formulation as a system of conservation laws. For first-order logarithmic forward–forward MFG, we establish the existence of a global solution. Then, we consider a class of explicit solutions and show the existence of shocks. Finally, we examine parabolic forward–forward MFGs and establish the long-time convergence of the solutions.
Mean-field study of $^{12}$C+$^{12}$C fusion
Chien, Le Hoang; Khoa, Dao T
2016-01-01
The nuclear mean-field potential arising from the $^{12}$C+$^{12}$C interaction at the low energies relevant for the astrophysical carbon burning process has been constructed within the double-folding model, using the realistic nuclear ground-state density of the $^{12}$C nucleus and the effective M3Y nucleon-nucleon (NN) interaction constructed from the G-matrix of the Paris (free) NN potential. To explore the nuclear medium effect, both the original density independent M3Y-Paris interaction and its density dependent CDM3Y6 version have been used in the folding model calculation of the $^{12}$C+$^{12}$C potential. The folded potentials at the different energies were used in the optical model description of the elastic $^{12}$C+$^{12}$C scattering at the energies around and below the Coulomb barrier, as well as in the barrier penetration model to estimate the fusion cross section and astrophysical $S$ factor of the $^{12}$C+$^{12}$C reactions at the low energies. The obtained results are in good agreement wit...
Individual based and mean-field modeling of direct aggregation
Burger, Martin
2013-10-01
We introduce two models of biological aggregation, based on randomly moving particles with individual stochasticity depending on the perceived average population density in their neighborhood. In the firstorder model the location of each individual is subject to a density-dependent random walk, while in the second-order model the density-dependent random walk acts on the velocity variable, together with a density-dependent damping term. The main novelty of our models is that we do not assume any explicit aggregative force acting on the individuals; instead, aggregation is obtained exclusively by reducing the individual stochasticity in response to higher perceived density. We formally derive the corresponding mean-field limits, leading to nonlocal degenerate diffusions. Then, we carry out the mathematical analysis of the first-order model, in particular, we prove the existence of weak solutions and show that it allows for measure-valued steady states. We also perform linear stability analysis and identify conditions for pattern formation. Moreover, we discuss the role of the nonlocality for well-posedness of the first-order model. Finally, we present results of numerical simulations for both the first- and second-order model on the individual-based and continuum levels of description. 2012 Elsevier B.V. All rights reserved.
Real-space renormalized dynamical mean field theory
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.
Combining Few-Body Cluster Structures with Many-Body Mean-Field Methods
Hove, D.; Garrido, E.; Jensen, A. S.; Sarriguren, P.; Fynbo, H. O. U.; Fedorov, D. V.; Zinner, N. T.
2017-03-01
Nuclear cluster physics implicitly assumes a distinction between groups of degrees-of-freedom, that is the (frozen) intrinsic and (explicitly treated) relative cluster motion. We formulate a realistic and practical method to describe the coupled motion of these two sets of degrees-of-freedom. We derive a coupled set of differential equations for the system using the phenomenologically adjusted effective in-medium Skyrme type of nucleon-nucleon interaction. We select a two-nucleon plus core system where the mean-field approximation corresponding to the Skyrme interaction is used for the core. A hyperspherical adiabatic expansion of the Faddeev equations is used for the relative cluster motion. We shall specifically compare both the structure and the decay mechanism found from the traditional three-body calculations with the result using the new boundary condition provided by the full microscopic structure at small distance. The extended Hilbert space guaranties an improved wave function compared to both mean-field and three-body solutions. We shall investigate the structures and decay mechanism of ^{22}C (^{20}C+n+n). In conclusion, we have developed a method combining nuclear few- and many-body techniques without losing the descriptive power of each approximation at medium-to-large distances and small distances respectively. The coupled set of equations are solved self-consistently, and both structure and dynamic evolution are studied.
Mean field lattice model for adsorption isotherms in zeolite NaA
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.
Relativistic Quantum Communication
Hosler, Dominic
2013-01-01
In this Ph.D. thesis, I investigate the communication abilities of non-inertial observers and the precision to which they can measure parametrized states. I introduce relativistic quantum field theory with field quantisation, and the definition and transformations of mode functions in Minkowski, Schwarzschild and Rindler spaces. I introduce information theory by discussing the nature of information, defining the entropic information measures, and highlighting the differences between classical and quantum information. I review the field of relativistic quantum information. We investigate the communication abilities of an inertial observer to a relativistic observer hovering above a Schwarzschild black hole, using the Rindler approximation. We compare both classical communication and quantum entanglement generation of the state merging protocol, for both the single and dual rail encodings. We find that while classical communication remains finite right up to the horizon, the quantum entanglement generation tend...
Maximizing Influence in an Ising Network: A Mean-Field Optimal Solution
Lynn, Christopher
2016-01-01
The problem of influence maximization in social networks has typically been studied in the context of contagion models and irreversible processes. In this paper, we consider an alternate model that treats individual opinions as spins in an Ising network at dynamic equilibrium. We formalize the Ising influence maximization (IIM) problem, which has a physical interpretation as the maximization of the magnetization given a budget of external magnetic field. Under the mean-field (MF) approximation, we develop a number of sufficient conditions for when the problem is convex and exactly solvable, and we provide a gradient ascent algorithm that efficiently achieves an $\\epsilon$-approximation to the optimal solution. We show that optimal strategies exhibit a phase transition from focusing influence on high-degree individuals at high interaction strengths to spreading influence among low-degree individuals at low interaction strengths. We also establish a number of novel results about the structure of steady-states i...
Rodrigues, Serafim [Department of Mathematical Sciences, Loughborough University, Leicestershire, LE11 3TU (United Kingdom); Terry, John R. [Department of Mathematical Sciences, Loughborough University, Leicestershire, LE11 3TU (United Kingdom)]. E-mail: j.r.terry@lboro.ac.uk; Breakspear, Michael [Black Dog Institute, Randwick, NSW 2031 (Australia); School of Psychiatry, UNSW, NSW 2030 (Australia)
2006-07-10
In this Letter, the genesis of spike-wave activity-a hallmark of many generalized epileptic seizures-is investigated in a reduced mean-field model of human neural activity. Drawing upon brain modelling and dynamical systems theory, we demonstrate that the thalamic circuitry of the system is crucial for the generation of these abnormal rhythms, observing that the combination of inhibition from reticular nuclei and excitation from the cortical signal, interplay to generate the spike-wave oscillation. The mechanism revealed provides an explanation of why approaches based on linear stability and Heaviside approximations to the activation function have failed to explain the phenomena of spike-wave behaviour in mean-field models. A mathematical understanding of this transition is a crucial step towards relating spiking network models and mean-field approaches to human brain modelling.
Kaki, K
2001-01-01
We calculate proton elastic scattering with sup 5 sup 8 Ni and sup 1 sup 2 sup 0 Sn at various intermediate energies with relativistic impulse approximation (RIA). We use the ground-state wave functions of the relativistic mean-field (RMF) calculation with the use of the TMA parameter set. We found good agreement with experimental data for the elastic scattering observables. In addition to the standard scalar and vector densities, we include also the tensor density. We study the Pauli effect and the vacuum polarization effect on the elastic scattering observables using the prescription of Horowitz and Serot at lower energy.
Conservation in two-particle self-consistent extensions of dynamical mean-field theory
Krien, Friedrich; van Loon, Erik G. C. P.; Hafermann, Hartmut; Otsuki, Junya; Katsnelson, Mikhail I.; Lichtenstein, Alexander I.
2017-08-01
Extensions of dynamical mean-field theory (DMFT) make use of quantum impurity models as nonperturbative and exactly solvable reference systems which are essential to treat the strong electronic correlations. Through the introduction of retarded interactions on the impurity, these approximations can be made two-particle self-consistent. This is of interest for the Hubbard model because it allows to suppress the antiferromagnetic phase transition in two dimensions in accordance with the Mermin-Wagner theorem, and to include the effects of bosonic fluctuations. For a physically sound description of the latter, the approximation should be conserving. In this paper, we show that the mutual requirements of two-particle self-consistency and conservation lead to fundamental problems. For an approximation that is two-particle self-consistent in the charge and longitudinal spin channels, the double occupancy of the lattice and the impurity is no longer consistent when computed from single-particle properties. For the case of self-consistency in the charge and longitudinal as well as transversal spin channels, these requirements are even mutually exclusive so that no conserving approximation can exist. We illustrate these findings for a two-particle self-consistent and conserving DMFT approximation.
Generalized One-Dimensional Point Interaction in Relativistic and Non-relativistic Quantum Mechanics
Shigehara, T; Mishima, T; Cheon, T; Cheon, Taksu
1999-01-01
We first give the solution for the local approximation of a four parameter family of generalized one-dimensional point interactions within the framework of non-relativistic model with three neighboring $\\delta$ functions. We also discuss the problem within relativistic (Dirac) framework and give the solution for a three parameter family. It gives a physical interpretation for so-called high energy substantially differ between non-relativistic and relativistic cases.
Relativistic corrections to molecular dynamic dipole polarizabilities
Kirpekar, Sheela; Oddershede, Jens; Jensen, Hans Jørgen Aagaard
1995-01-01
Using response function methods we report calculations of the dynamic isotropic polarizability of SnH4 and PbH4 and of the relativistic corrections to it in the random phase approximation and at the correlated multiconfigurational linear response level of approximation. All relativistic corrections...
Hamaya, S.; Maeda, H.; Funaki, M.; Fukui, H.
2008-12-01
The relativistic calculation of nuclear magnetic shielding tensors in hydrogen halides is performed using the second-order regular approximation to the normalized elimination of the small component (SORA-NESC) method with the inclusion of the perturbation terms from the metric operator. This computational scheme is denoted as SORA-Met. The SORA-Met calculation yields anisotropies, Δσ =σ∥-σ⊥, for the halogen nuclei in hydrogen halides that are too small. In the NESC theory, the small component of the spinor is combined to the large component via the operator σ⃗ṡπ⃗U/2c, in which π⃗=p⃗+A⃗, U is a nonunitary transformation operator, and c ≅137.036 a.u. is the velocity of light. The operator U depends on the vector potential A⃗ (i.e., the magnetic perturbations in the system) with the leading order c-2 and the magnetic perturbation terms of U contribute to the Hamiltonian and metric operators of the system in the leading order c-4. It is shown that the small Δσ for halogen nuclei found in our previous studies is related to the neglect of the U(0,1) perturbation operator of U, which is independent of the external magnetic field and of the first order with respect to the nuclear magnetic dipole moment. Introduction of gauge-including atomic orbitals and a finite-size nuclear model is also discussed.
Coagulation kinetics beyond mean field theory using an optimised Poisson representation.
Burnett, James; Ford, Ian J
2015-05-21
Binary particle coagulation can be modelled as the repeated random process of the combination of two particles to form a third. The kinetics may be represented by population rate equations based on a mean field assumption, according to which the rate of aggregation is taken to be proportional to the product of the mean populations of the two participants, but this can be a poor approximation when the mean populations are small. However, using the Poisson representation, it is possible to derive a set of rate equations that go beyond mean field theory, describing pseudo-populations that are continuous, noisy, and complex, but where averaging over the noise and initial conditions gives the mean of the physical population. Such an approach is explored for the simple case of a size-independent rate of coagulation between particles. Analytical results are compared with numerical computations and with results derived by other means. In the numerical work, we encounter instabilities that can be eliminated using a suitable "gauge" transformation of the problem [P. D. Drummond, Eur. Phys. J. B 38, 617 (2004)] which we show to be equivalent to the application of the Cameron-Martin-Girsanov formula describing a shift in a probability measure. The cost of such a procedure is to introduce additional statistical noise into the numerical results, but we identify an optimised gauge transformation where this difficulty is minimal for the main properties of interest. For more complicated systems, such an approach is likely to be computationally cheaper than Monte Carlo simulation.
Non-perturbative heterogeneous mean-field approach to epidemic spreading in complex networks
Gomez, Sergio; Moreno, Yamir; Arenas, Alex
2011-01-01
Since roughly a decade ago, network science has focused among others on the problem of how the spreading of diseases depends on structural patterns. Here, we contribute to further advance our understanding of epidemic spreading processes by proposing a non-perturbative formulation of the heterogeneous mean field approach that has been commonly used in the physics literature to deal with this kind of spreading phenomena. The non-perturbative equations we propose have no assumption about the proximity of the system to the epidemic threshold, nor any linear approximation of the dynamics. In particular, we first develop a probabilistic description at the node level of the epidemic propagation for the so-called susceptible-infected-susceptible family of models, and after we derive the corresponding heterogeneous mean-field approach. We propose to use the full extension of the approach instead of pruning the expansion to first order, which leads to a non-perturbative formulation that can be solved by fixed point it...
Elementary proof of convergence to the mean-field model for the SIR process.
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.
Quantum de Finetti theorems and mean-field theory from quantum phase space representations
Trimborn, F.; Werner, R. F.; Witthaut, D.
2016-04-01
We introduce the number-conserving quantum phase space description as a versatile tool to address fundamental aspects of quantum many-body systems. Using phase space methods we prove two alternative versions of the quantum de Finetti theorem for finite-dimensional bosonic quantum systems, which states that a reduced density matrix of a many-body quantum state can be approximated by a convex combination of product states where the error is proportional to the inverse particle number. This theorem provides a formal justification for the mean-field description of many-body quantum systems, as it shows that quantum correlations can be neglected for the calculation of few-body observables when the particle number is large. Furthermore we discuss methods to derive the exact evolution equations for quantum phase space distribution functions as well as upper and lower bounds for the ground state energy. As an important example, we consider the Bose-Hubbard model and show that the mean-field dynamics is given by a classical phase space flow equivalent to the discrete Gross-Pitaevskii equation.
Effects of anisotropy of turbulent convection in mean-field solar dynamo models
Pipin, V V
2013-01-01
We study how anisotropy of turbulent convection affects diffusion of large-scale magnetic fields and the dynamo process on the Sun. The effect of anisotropy is calculated in a mean-field magneto-hydrodynamics framework using the minimal $\\tau$-approximation. We examine two types of mean-field dynamo models: the well-known benchmark flux-transport model, and a distributed-dynamo model with the subsurface rotational shear layer. For both models we investigate effects of the double-cell meridional circulation, recently suggested by helioseismology. We introduce a parameter of anisotropy as a ratio of the radial and horizontal intensity of turbulent mixing, to characterize the anisotropy effects. It is found that the anisotropy of turbulent convection affects the distribution of magnetic fields inside the convection zone. The concentration of the magnetic flux near the bottom and top boundaries of the convection zone is greater when the anisotropy is stronger. It is shown that the critical dynamo number and the d...
Stable oscillations of a predator-prey probabilistic cellular automaton: a mean-field approach
Tome, Tania; Carvalho, Kelly C de [Instituto de FIsica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970 Sao Paulo (Brazil)
2007-10-26
We analyze a probabilistic cellular automaton describing the dynamics of coexistence of a predator-prey system. The individuals of each species are localized over the sites of a lattice and the local stochastic updating rules are inspired by the processes of the Lotka-Volterra model. Two levels of mean-field approximations are set up. The simple approximation is equivalent to an extended patch model, a simple metapopulation model with patches colonized by prey, patches colonized by predators and empty patches. This approximation is capable of describing the limited available space for species occupancy. The pair approximation is moreover able to describe two types of coexistence of prey and predators: one where population densities are constant in time and another displaying self-sustained time oscillations of the population densities. The oscillations are associated with limit cycles and arise through a Hopf bifurcation. They are stable against changes in the initial conditions and, in this sense, they differ from the Lotka-Volterra cycles which depend on initial conditions. In this respect, the present model is biologically more realistic than the Lotka-Volterra model.
Resonances and reactions from mean-field dynamics
Stevenson P. D.
2016-01-01
Full Text Available The time-dependent version of nuclear density functional theory, using functionals derived from Skyrme interactions, is able to approximately describe nuclear dynamics. We present time-dependent results of calculations of dipole resonances, concentrating on excitations of valence neutrons against a proton plus neutron core in the neutron-rich doubly-magic 132Sn nucleus, and results of collision dynamics, highlighting potential routes to ternary fusion, with the example of a collision of 48Ca+48Ca+208Pb resulting in a compound nucleus of element 120 stable against immediate fission.
Luciano, Rezzolla
2013-01-01
Relativistic hydrodynamics is a very successful theoretical framework to describe the dynamics of matter from scales as small as those of colliding elementary particles, up to the largest scales in the universe. This book provides an up-to-date, lively, and approachable introduction to the mathematical formalism, numerical techniques, and applications of relativistic hydrodynamics. The topic is typically covered either by very formal or by very phenomenological books, but is instead presented here in a form that will be appreciated both by students and researchers in the field. The topics covered in the book are the results of work carried out over the last 40 years, which can be found in rather technical research articles with dissimilar notations and styles. The book is not just a collection of scattered information, but a well-organized description of relativistic hydrodynamics, from the basic principles of statistical kinetic theory, down to the technical aspects of numerical methods devised for the solut...
Mean-field concept and direct numerical simulations of rotating magnetoconvection and the geodynamo
Schrinner, M; Schmitt, D; Rheinhardt, M; Christensen, U R
2006-01-01
A comparison is made between mean-field models and direct numerical simulations of rotating magnetoconvection and the geodynamo. The mean-field coefficients are calculated with the fluid velocity taken from the direct numerical simulations. The magnetic fields resulting from mean-field models are then compared with the mean magnetic field from the direct numerical simulations.
Shimizu, Y R; Shimizu, Yoshifumi R.; Matsuyanagi, Kenichi
2000-01-01
Diabatic description of rotational bands provides a clear-cut picture for understanding the back-bending phenomena, where the internal structure of the yrast band changes dramatically as a function of angular momentum. A microscopic framework to obtain the diabatic bands within the mean-field approximation is presented by making use of the selfconsistent collective coordinate method. Applying the framework, both the ground state rotational bands and the Stockholm bands are studied systematically for the rare-earth deformed nuclei. An overall agreement has been achieved between the calculated and observed rotational spectra. It is also shown that the inclusion of the double-stretched quadrupole-pairing interaction is crucial to obtain an overall agreement for the even-odd mass differences and the rotational spectra simultaneously.
Second-order corrections to mean field evolution for weakly interacting Bosons. I
Grillakis, Manoussos G; Margetis, Dionisios
2009-01-01
Inspired by the works of Rodnianski and Schlein and Wu, we derive a new nonlinear Schr\\"odinger equation that describes a second-order correction to the usual tensor product (mean-field) approximation for the Hamiltonian evolution of a many-particle system in Bose-Einstein condensation. We show that our new equation, if it has solutions with appropriate smoothness and decay properties, implies a new Fock space estimate. We also show that for an interaction potential $v(x)= \\epsilon \\chi(x) |x|^{-1}$, where $\\epsilon$ is sufficiently small and $\\chi \\in C_0^{\\infty}$, our program can be easily implemented locally in time. We leave global in time issues, more singular potentials and sophisticated estimates for a subsequent part (part II) of this paper.
Mean-field state population study for iron-based superconductors
Wang, Zhigang; Fu, Zhen-Guo; Zheng, Fa-Wei; Zhang, Ping
2017-02-01
The occupation number distribution in momentum space are theoretically studied within a two-orbital model, which can be unified describing the low-energy physics of the iron pnictides and iron chalcogenides. The mean-field approximation of Hubbard interaction is employed. By tuning the hopping parameters, the difference between the iron pnictides and iron chalcogenides in their occupation number distribution behavior can be clearly observed. The results show that when the pairing interaction tends to zero, the occupation number n (k) ≈ 0 at Γ point for iron chalcogenides while n (k) ≈ 2 at Γ point for iron pnictides. By increasing the strength of the pairing interaction to a large value, the change of n (k) at Γ point for iron chalcogenides (pnictides) is remarkable (unremarkable). In addition, we find that the effect of the nearest-neighbor coupling between the two layers, contained in the S4 model [Hu and Hao, (2012) [33
β-decay of magic nuclei: Beyond mean-field description
Niu, Yifei, E-mail: nyfster@gmail.com [Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621900 (China); INFN, Sezione di Milano, via Celoria 16, I-20133 Milano (Italy); Niu, Zhongming [School of Physics and Material Science, Anhui University, Hefei 230601 (China); Colò, Gianluca [Dipartimento di Fisica, Università degli Studi di Milano, via Celoria 16, I-20133 Milano (Italy); INFN, Sezione di Milano, via Celoria 16, I-20133 Milano (Italy); Vigezzi, Enrico [INFN, Sezione di Milano, via Celoria 16, I-20133 Milano (Italy)
2015-10-15
Nuclear β-decay plays an important role not only in nuclear physics but also in astrophysics. The widely used self-consistent Random Phase Approximation (RPA) models tend to overestimate the half-lives of magic nuclei. To overcome this problem, we go beyond the mean-field description and include the effects of particle-vibration coupling (PVC) on top of the RPA model. The β-decay half-lives of {sup 34}Si, {sup 68}Ni, {sup 78}Ni, and {sup 132}Sn are studied within this approach in the case of the Skyrme interaction SkM*. It is found that the low-lying Gamow-Teller (GT) strength is shifted downwards with the inclusion of the PVC effect, and as a consequence, the half-lives are reduced due to the increase of the phase space available for β-decay, which leads to a good agreement between theoretical and experimental lifetimes.
Hall current effects in mean-field dynamo theory
Lingam, Manasvi
2016-01-01
The role of the Hall term on large scale dynamo action is investigated by means of the First Order Smoothing Approximation. It is shown that the standard $\\alpha$ coefficient is altered, and is zero when a specific double Beltrami state is attained, in contrast to the Alfv\\'enic state for MHD dynamos. The $\\beta$ coefficient is no longer positive definite, and thereby enables dynamo action even if $\\alpha$-quenching were to operate. The similarities and differences with the (magnetic) shear-current effect are pointed out, and a mechanism that may be potentially responsible for $\\beta < 0$ is advanced. The results are compared against previous studies, and their astrophysical relevance is also highlighted.
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.
Sahoo, Raghunath
2016-01-01
This lecture note covers Relativistic Kinematics, which is very useful for the beginners in the field of high-energy physics. A very practical approach has been taken, which answers "why and how" of the kinematics useful for students working in the related areas.
Mean-field dynamo in a turbulence with shear and kinetic helicity fluctuations.
Kleeorin, Nathan; Rogachevskii, Igor
2008-03-01
We study the effects of kinetic helicity fluctuations in a turbulence with large-scale shear using two different approaches: the spectral tau approximation and the second-order correlation approximation (or first-order smoothing approximation). These two approaches demonstrate that homogeneous kinetic helicity fluctuations alone with zero mean value in a sheared homogeneous turbulence cannot cause a large-scale dynamo. A mean-field dynamo is possible when the kinetic helicity fluctuations are inhomogeneous, which causes a nonzero mean alpha effect in a sheared turbulence. On the other hand, the shear-current effect can generate a large-scale magnetic field even in a homogeneous nonhelical turbulence with large-scale shear. This effect was investigated previously for large hydrodynamic and magnetic Reynolds numbers. In this study we examine the threshold required for the shear-current dynamo versus Reynolds number. We demonstrate that there is no need for a developed inertial range in order to maintain the shear-current dynamo (e.g., the threshold in the Reynolds number is of the order of 1).
Archer, Andrew J.; Chacko, Blesson; Evans, Robert
2017-07-01
In classical density functional theory (DFT), the part of the Helmholtz free energy functional arising from attractive inter-particle interactions is often treated in a mean-field or van der Waals approximation. On the face of it, this is a somewhat crude treatment as the resulting functional generates the simple random phase approximation (RPA) for the bulk fluid pair direct correlation function. We explain why using standard mean-field DFT to describe inhomogeneous fluid structure and thermodynamics is more accurate than one might expect based on this observation. By considering the pair correlation function g(x) and structure factor S(k) of a one-dimensional model fluid, for which exact results are available, we show that the mean-field DFT, employed within the test-particle procedure, yields results much superior to those from the RPA closure of the bulk Ornstein-Zernike equation. We argue that one should not judge the quality of a DFT based solely on the approximation it generates for the bulk pair direct correlation function.
Lu, K Q; Li, Z P; Yao, J M; Meng, J
2015-01-01
We report the first global study of dynamic correlation energies (DCEs) associated with rotational motion and quadrupole shape vibrational motion in a covariant energy density functional (CEDF) for 575 even-even nuclei with proton numbers ranging from $Z=8$ to $Z=108$ by solving a five-dimensional collective Hamiltonian, the collective parameters of which are determined from triaxial relativistic mean-field plus BCS calculation using the PC-PK1 force. After taking into account these beyond mean-field DCEs, the root-mean-square (rms) deviation with respect to nuclear masses is reduced significantly down to 1.14 MeV, which is smaller than those of other successful CEDFs: NL3* (2.96 MeV), DD-ME2 (2.39 MeV), DD-ME$\\delta$ (2.29 MeV) and DD-PC1 (2.01 MeV). Moreover, the rms deviation for two-nucleon separation energies is reduced by $\\sim34\\%$ in comparison with cranking prescription.
Erler, Bastian
2012-07-18
Realistic nucleon-nucleon interactions transformed via the Unitary Correlation Operator Method (UCOM) or the Similarity Renormalization Group (SRG) have proven to be a suitable starting point for the description of closed-shell nuclei via mean-field methods like Hartree-Fock (HF). This allows the treatment of a number of heavy nuclei with realistic nucleon-nucleon interactions, which would otherwise only be possible with phenomenological interactions. To include three-nucleon forces in an approximate way, the UCOM or SRG transformed interactions can be augmented by a three-body contact interaction, which is necessary to reproduce measured charge radii. However, many interesting nuclei, including those near the neutron drip line, are far away from closed shells. These nuclei are of great importance for modeling nucleosynthesis processes in the universe, but experiments can only be performed at a few research facilities. In this work, the Hartree Fock (HF) approach with realistic interactions is extended to light deformed nuclei. Pairing correlations are not taken into account. A crucial step in this process is to allow deformed ground states on the mean-field level, as only nuclei with at least one closed shell can be described with spherical HF ground states. To restore the rotational symmetry in the lab frame, exact angular-momentum projection (AMP) is implemented. Constrained HF calculations are used for an approximate variation after projection approach. The AMP-HF description of open-shell nuclei is on par with the pure HF description of closed-shell nuclei. Charge-radii and systematics of binding energies agree well with experiment. However, missing correlations, lead to an underestimated absolute value of the binding energy. Projection on higher angular momenta approximately reproduces the energy systematics of rotational bands. To describe collective excitations, the Random Phase Approximation (RPA) constitutes a well tested approach, which can also be
Kouno, H.; Kakuta, N.; Noda, N.; Koide, K.; Mitsumori, T.; Hasegawa, A.; Nakano, M. (Department of Physics, Saga University, Saga 840 (Japan))
1995-04-01
We have studied the equations of state of nuclear matter using the nonlinear [sigma]-[omega] model. At the normal density, there is a strong correlation among the effective nucleon mass [ital M][sub 0][sup *], the incompressibility, [ital K] and the third derivative [ital K][prime] of binding energy. The results are compared with the empirical analysis of the giant isoscalar monopole resonances data. It is difficult to fit the data when [ital K][approx lt]200 MeV, using the model. It is also found that [ital K]=300[plus minus]50 MeV is favorable to account for the volume-symmetry properties of nuclear matter.
Alpha-decay chains of $^{288}_{173}115$ and $^{287}_{172}115$ in the Relativistic Mean Field theory
Geng, L S; Meng, J
2003-01-01
The results of experiments designed to synthesize element 115 in the $^{243}$Am+$^{48}$Ca reaction are reported at Dubna in Russia \\cite{ogan.03}. With a beam dose of $4.3\\times 10^{18}$ 248-MeV $^{48}$Ca projectiles, three similar decay chains consisting of five consecutive $\\alpha$-decays are observed. At a higher bombarding energy of 253 MeV, with an equal $^{48}$Ca beam dose, a different decay chain of four consecutive $\\alpha$-decays are detected. The decay properties of these synthesized nuclei are consistent with consecutive $\\alpha$-decay originating from the parent isotopes of the new element 115, $^{288}115$ and $^{287}115$, respectively. In the present work, the recently developed deformed RMF+BCS method with a density-independent delta-function interaction in the pairing channel is applied to the analysis of these newly synthesized superheavy nuclei $^{288}115$, $^{287}115$, and their $\\alpha$-decay daughter nuclei. The calculated $\\alpha$-decay energies and half-lives agree well with the experime...
Magnetic Field Line Random Walk in Isotropic Turbulence with Varying Mean Field
Sonsrettee, W.; Subedi, P.; Ruffolo, D.; Matthaeus, W. H.; Snodin, A. P.; Wongpan, P.; Chuychai, P.; Rowlands, G.; Vyas, S.
2016-08-01
In astrophysical plasmas, the magnetic field line random walk (FLRW) plays an important role in guiding particle transport. The FLRW behavior is scaled by the Kubo number R=(b/{B}0)({{\\ell }}\\parallel /{{\\ell }}\\perp ) for rms magnetic fluctuation b, large-scale mean field {{\\boldsymbol{B}}}0, and coherence scales parallel ({{\\ell }}\\parallel ) and perpendicular ({{\\ell }}\\perp ) to {{\\boldsymbol{B}}}0. Here we use a nonperturbative analytic framework based on Corrsin’s hypothesis, together with direct computer simulations, to examine the R-scaling of the FLRW for varying B 0 with finite b and isotropic fluctuations with {{\\ell }}\\parallel /{{\\ell }}\\perp =1, instead of the well-studied route of varying {{\\ell }}\\parallel /{{\\ell }}\\perp for b \\ll {B}0. The FLRW for isotropic magnetic fluctuations is also of astrophysical interest regarding transport processes in the interstellar medium. With a mean field, fluctuations may have variance anisotropy, so we consider limiting cases of isotropic variance and transverse variance (with b z = 0). We obtain analytic theories, and closed-form solutions for extreme cases. Padé approximants are provided to interpolate all versions of theory and simulations to any B 0. We demonstrate that, for isotropic turbulence, Corrsin-based theories generally work well, and with increasing R there is a transition from quasilinear to Bohm diffusion. This holds even with b z = 0, when different routes to R\\to ∞ are mathematically equivalent; in contrast with previous studies, we find that a Corrsin-based theory with random ballistic decorrelation works well even up to R = 400, where the effects of trapping are barely perceptible in simulation results.
Active matter beyond mean-field: ring-kinetic theory for self-propelled particles.
Chou, Yen-Liang; Ihle, Thomas
2015-02-01
Recently, Hanke et al. [Phys. Rev. E 88, 052309 (2013)] showed that mean-field kinetic theory fails to describe collective motion in soft active colloids and that correlations must not be neglected. Correlation effects are also expected to be essential in systems of biofilaments driven by molecular motors and in swarms of midges. To obtain correlations in an active matter system from first principles, we derive a ring-kinetic theory for Vicsek-style models of self-propelled agents from the exact N-particle evolution equation in phase space. The theory goes beyond mean-field and does not rely on Boltzmann's approximation of molecular chaos. It can handle precollisional correlations and cluster formation, which are both important to understand the phase transition to collective motion. We propose a diagrammatic technique to perform a small-density expansion of the collision operator and derive the first two equations of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. An algorithm is presented that numerically solves the evolution equation for the two-particle correlations on a lattice. Agent-based simulations are performed and informative quantities such as orientational and density correlation functions are compared with those obtained by ring-kinetic theory. Excellent quantitative agreement between simulations and theory is found at not-too-small noises and mean free paths. This shows that there are parameter ranges in Vicsek-like models where the correlated closure of the BBGKY hierarchy gives correct and nontrivial results. We calculate the dependence of the orientational correlations on distance in the disordered phase and find that it seems to be consistent with a power law with an exponent around -1.8, followed by an exponential decay. General limitations of the kinetic theory and its numerical solution are discussed.
Coagulation kinetics beyond mean field theory using an optimised Poisson representation
Burnett, James [Department of Mathematics, UCL, Gower Street, London WC1E 6BT (United Kingdom); Ford, Ian J. [Department of Physics and Astronomy, UCL, Gower Street, London WC1E 6BT (United Kingdom)
2015-05-21
Binary particle coagulation can be modelled as the repeated random process of the combination of two particles to form a third. The kinetics may be represented by population rate equations based on a mean field assumption, according to which the rate of aggregation is taken to be proportional to the product of the mean populations of the two participants, but this can be a poor approximation when the mean populations are small. However, using the Poisson representation, it is possible to derive a set of rate equations that go beyond mean field theory, describing pseudo-populations that are continuous, noisy, and complex, but where averaging over the noise and initial conditions gives the mean of the physical population. Such an approach is explored for the simple case of a size-independent rate of coagulation between particles. Analytical results are compared with numerical computations and with results derived by other means. In the numerical work, we encounter instabilities that can be eliminated using a suitable “gauge” transformation of the problem [P. D. Drummond, Eur. Phys. J. B 38, 617 (2004)] which we show to be equivalent to the application of the Cameron-Martin-Girsanov formula describing a shift in a probability measure. The cost of such a procedure is to introduce additional statistical noise into the numerical results, but we identify an optimised gauge transformation where this difficulty is minimal for the main properties of interest. For more complicated systems, such an approach is likely to be computationally cheaper than Monte Carlo simulation.
Hakim, Rémi
1994-01-01
Il existe à l'heure actuelle un certain nombre de théories relativistes de la gravitation compatibles avec l'expérience et l'observation. Toutefois, la relativité générale d'Einstein fut historiquement la première à fournir des résultats théoriques corrects en accord précis avec les faits.
Jones, Bernard J. T.; Markovic, Dragoljub
1997-06-01
Preface; Prologue: Conference overview Bernard Carr; Part I. The Universe At Large and Very Large Redshifts: 2. The size and age of the Universe Gustav A. Tammann; 3. Active galaxies at large redshifts Malcolm S. Longair; 4. Observational cosmology with the cosmic microwave background George F. Smoot; 5. Future prospects in measuring the CMB power spectrum Philip M. Lubin; 6. Inflationary cosmology Michael S. Turner; 7. The signature of the Universe Bernard J. T. Jones; 8. Theory of large-scale structure Sergei F. Shandarin; 9. The origin of matter in the universe Lev A. Kofman; 10. New guises for cold-dark matter suspects Edward W. Kolb; Part II. Physics and Astrophysics Of Relativistic Compact Objects: 11. On the unification of gravitational and inertial forces Donald Lynden-Bell; 12. Internal structure of astrophysical black holes Werner Israel; 13. Black hole entropy: external facade and internal reality Valery Frolov; 14. Accretion disks around black holes Marek A. Abramowicz; 15. Black hole X-ray transients J. Craig Wheeler; 16. X-rays and gamma rays from active galactic nuclei Roland Svensson; 17. Gamma-ray bursts: a challenge to relativistic astrophysics Martin Rees; 18. Probing black holes and other exotic objects with gravitational waves Kip Thorne; Epilogue: the past and future of relativistic astrophysics Igor D. Novikov; I. D. Novikov's scientific papers and books.
Linear $\\Sigma$ Model in the Gaussian Functional Approximation
Nakamura, I
2001-01-01
We apply a self-consistent relativistic mean-field variational ``Gaussian functional'' (or Hartree) approximation to the linear $\\sigma$ model with spontaneously and explicitly broken chiral O(4) symmetry. We set up the self-consistency, or ``gap'' and the Bethe-Salpeter equations. We check and confirm the chiral Ward-Takahashi identities, among them the Nambu-Goldstone theorem and the (partial) axial current conservation [CAC], both in and away from the chiral limit. With explicit chiral symmetry breaking we confirm the Dashen relation for the pion mass and partial CAC. We solve numerically the gap and Bethe-Salpeter equations, discuss the solutions' properties and the particle content of the theory.
Bassi, G.; /Liverpool U. /Cockroft Inst.; Ellison, J.A.; Heinemann, K.; /New Mexico U.; Warnock, R.; /SLAC
2009-05-07
Bunch compressors, designed to increase the peak current, can lead to a microbunching instability with detrimental effects on the beam quality. This is a major concern for free electron lasers (FELs) where very bright electron beams are required, i.e. beams with low emittance and energy spread. In this paper, we apply our self-consistent, parallel solver to study the microbunching instability in the first bunch compressor system of FERMI{at}Elettra. Our basic model is a 2D Vlasov-Maxwell system. We treat the beam evolution through a bunch compressor using our Monte Carlo mean field approximation. We randomly generate N points from an initial phase space density. We then calculate the charge density using a smooth density estimation procedure, from statistics, based on Fourier series. The electric and magnetic fields are calculated from the smooth charge/current density using a novel field formula that avoids singularities by using the retarded time as a variable of integration. The points are then moved forward in small time steps using the beam frame equations of motion, with the fields frozen during a time step, and a new charge density is determined using our density estimation procedure. We try to choose N large enough so that the charge density is a good approximation to the density that would be obtained from solving the 2D Vlasov-Maxwell system exactly. We call this method the Monte Carlo Particle (MCP) method.
Brownian regime of finite-N corrections to particle motion in the XY Hamiltonian mean field model
Ribeiro, Bruno V.; Amato, Marco A.; Elskens, Yves
2016-08-01
We study the dynamics of the N-particle system evolving in the XY Hamiltonian mean field (HMF) model for a repulsive potential, when no phase transition occurs. Starting from a homogeneous distribution, particles evolve in a mean field created by the interaction with all others. This interaction does not change the homogeneous state of the system, and particle motion is approximately ballistic with small corrections. For initial particle data approaching a waterbag, it is explicitly proved that corrections to the ballistic velocities are in the form of independent Brownian noises over a time scale diverging not slower than {N}2/5 as N\\to ∞ , which proves the propagation of molecular chaos. Molecular dynamics simulations of the XY-HMF model confirm our analytical findings.
Brownian regime of finite-N corrections to particle motion in the XY hamiltonian mean field model
Ribeiro, Bruno V; Elskens, Yves
2016-01-01
We study the dynamics of the N-particle system evolving in the XY hamiltonian mean field (HMF) model for a repulsive potential, when no phase transition occurs. Starting from a homogeneous distribution, particles evolve in a mean field created by the interaction with all others. This interaction does not change the homogeneous state of the system, and particle motion is approximately ballistic with small corrections. For initial particle data approaching a waterbag, it is explicitly proved that corrections to the ballistic velocities are in the form of independent brownian noises over a time scale diverging not slower than $N^{2/5}$ as $N \\to \\infty$, which proves the propagation of molecular chaos. Molecular dynamics simulations of the XY-HMF model confirm our analytical findings.
Exact mean-field theory of ionic solutions: non-Debye screening
Varela, Luis M.; García, Manuel; Mosquera, Víctor
2003-07-01
The main aim of this report is to analyze the equilibrium properties of primitive model (PM) ionic solutions in the formally exact mean-field formalism. Previously, we review the main theoretical and numerical results reported throughout the last century for homogeneous (electrolytes) and inhomogeneous (electric double layer, edl) ionic systems, starting with the classical mean-field theory of electrolytes due to Debye and Hückel (DH). In this formalism, the effective potential is derived from the Poisson-Boltzmann (PB) equation and its asymptotic behavior analyzed in the classical Debye theory of screening. The thermodynamic properties of electrolyte solutions are briefly reviewed in the DH formalism. The main analytical and numerical extensions of DH formalism are revised, ranging from the earliest extensions that overcome the linearization of the PB equation to the more sophisticated integral equation techniques introduced after the late 1960s. Some Monte Carlo and molecular dynamic simulations are also reviewed. The potential distributions in an inhomogeneous ionic system are studied in the classical PB framework, presenting the classical Gouy-Chapman (GC) theory of the electric double layer (edl) in a brief manner. The mean-field theory is adequately contextualized using field theoretic (FT) results and it is proven that the classical PB theory is recovered at the Gaussian or one-loop level of the exact FT, and a systematic way to obtain the corrections to the DH theory is derived. Particularly, it is proven following Kholodenko and Beyerlein that corrections to DH theory effectively lead to a renormalization of charges and Debye screening length. The main analytical and numerical results for this non-Debye screening length are reviewed, ranging from asymptotic expansions, self-consistent theory, nonlinear DH results and hypernetted chain (HNC) calculations. Finally, we study the exact mean-field theory of ionic solutions, the so-called dressed-ion theory
Exact mean-field theory of ionic solutions: non-Debye screening
Varela, L.M.; Garcia, Manuel; Mosquera, Victor
2003-07-01
The main aim of this report is to analyze the equilibrium properties of primitive model (PM) ionic solutions in the formally exact mean-field formalism. Previously, we review the main theoretical and numerical results reported throughout the last century for homogeneous (electrolytes) and inhomogeneous (electric double layer, edl) ionic systems, starting with the classical mean-field theory of electrolytes due to Debye and Hueckel (DH). In this formalism, the effective potential is derived from the Poisson-Boltzmann (PB) equation and its asymptotic behavior analyzed in the classical Debye theory of screening. The thermodynamic properties of electrolyte solutions are briefly reviewed in the DH formalism. The main analytical and numerical extensions of DH formalism are revised, ranging from the earliest extensions that overcome the linearization of the PB equation to the more sophisticated integral equation techniques introduced after the late 1960s. Some Monte Carlo and molecular dynamic simulations are also reviewed. The potential distributions in an inhomogeneous ionic system are studied in the classical PB framework, presenting the classical Gouy-Chapman (GC) theory of the electric double layer (edl) in a brief manner. The mean-field theory is adequately contextualized using field theoretic (FT) results and it is proven that the classical PB theory is recovered at the Gaussian or one-loop level of the exact FT, and a systematic way to obtain the corrections to the DH theory is derived. Particularly, it is proven following Kholodenko and Beyerlein that corrections to DH theory effectively lead to a renormalization of charges and Debye screening length. The main analytical and numerical results for this non-Debye screening length are reviewed, ranging from asymptotic expansions, self-consistent theory, nonlinear DH results and hypernetted chain (HNC) calculations. Finally, we study the exact mean-field theory of ionic solutions, the so-called dressed-ion theory
Investigation of Properties of Exotic Nuclei in Non-relativistic and Relativistic Models
2001-01-01
Properties of exotic nuclei are described by non-relativistic and relativistic models. The relativistic mean field theory predicts one proton halo in 26,27,28P and two proton halos in 27,28,29S, recently, one proton halo in 26,27,28P has been found experimentally in MSU lab. The relativistic Hartree-Fock theory has been used to investigate the contribution of Fock term and isovector mesons to the properties of exotic nuclei. It turns out that the influence of the Fock term and isovector mesons on the properties of neutron extremely rich nuclei is very different from that of near stable nuclei. Meanwhile, the deformed Hartree-Fock-Bogoliubov theory has been employed to describe the ground state properties of the isotopes for some light nuclei.
Amplitude pattern synthesis for conformal array antennas using mean-field neural networks
Castaldi, G.; Gerini, G.
2001-01-01
In this paper, we deal with the synthesis problem of conformai array antennas using a mean-field neural network. We applied a discrete version of mean-field neural network proposed by Vidyasagar [1], This technique is used to find the global minimum of the objective function, which represents the sq
Rigorous mean-field dynamics of lattice bosons: quenches from the Mott insulator
M. Snoek
2011-01-01
We provide a rigorous derivation of Gutzwiller mean-field dynamics for lattice bosons, showing that it is exact on fully connected lattices. We apply this formalism to quenches in the interaction parameter from the Mott insulator to the superfluid state. Although within mean-field the Mott insulator
On Mean-Field Theory of Quantum Phase Transition in Granular Superconductors
Simkin, M V
1996-01-01
In previous work on quantum phase transition in granular superconductors, where mean-field theory was used, an assumption was made that the order parameter as a function of the mean field is a convex up function. Though this is not always the case in phase transitions, this assumption must be verified, what is done in this article.
Gibbs Properties of the Fuzzy Potts Model on Trees and in Mean Field
Häggström, O.; Külske, C.
2004-01-01
We study Gibbs properties of the fuzzy Potts model in the mean field case (i.e. on a complete graph) and on trees. For the mean field case, a complete characterization of the set of temperatures for which non-Gibbsianness happens is given. The results for trees are somewhat less explicit, but we do
Mean-field theory of random-site q-state Potts models
van Enter, Aernout; Hemmen, Jan Leonard van; Pospiech, C.
1988-01-01
A class of random-site mean-field Potts models is introduced and solved exactly. The bifurcation properties of the resulting mean-field equations are analysed in detail. Particular emphasis is put on the relation between the solutions and the underlying symmetries of the model. It turns out that, in
Malik, G P
2016-01-01
Given the Debye temperature of an elemental superconductor (SC) and its Tc, BCS theory enables one to predict the value of its gap 0 at T = 0, or vice versa. This monograph shows that non-elemental SCs can be similarly dealt with via the generalized BCS equations (GBCSEs) which, given any two parameters of the set {Tc, 10, 20 > 10}, enable one to predict the third. Also given herein are new equations for the critical magnetic field and critical current density of an elemental and a non-elemental SC — equations that are derived directly from those that govern pairing in them. The monograph includes topics that are usually not covered in any one text on superconductivity, e.g., BCS-BEC crossover physics, the long-standing puzzle posed by SrTiO3, and heavy-fermion superconductors — all of which are still imperfectly understood and therefore continue to avidly engage theoreticians. It suggests that addressing the Tcs, s and other properties (e.g., number densities of charge carriers) of high-Tc SCs via GBCSE...
Relativistic and non-relativistic geodesic equations
Giambo' , R.; Mangiarotti, L.; Sardanashvily, G. [Camerino Univ., Camerino, MC (Italy). Dipt. di Matematica e Fisica
1999-07-01
It is shown that any dynamic equation on a configuration space of non-relativistic time-dependent mechanics is associated with connections on its tangent bundle. As a consequence, every non-relativistic dynamic equation can be seen as a geodesic equation with respect to a (non-linear) connection on this tangent bundle. Using this fact, the relationships between relativistic and non-relativistic equations of motion is studied.
Nuclear mean field and double-folding model of the nucleus-nucleus optical potential
Khoa, Dao T; Loan, Doan Thi; Loc, Bui Minh
2016-01-01
Realistic density dependent CDM3Yn versions of the M3Y interaction have been used in an extended Hartree-Fock (HF) calculation of nuclear matter (NM), with the nucleon single-particle potential determined from the total NM energy based on the Hugenholtz-van Hove theorem that gives rise naturally to a rearrangement term (RT). Using the RT of the single-nucleon potential obtained exactly at different NM densities, the density- and energy dependence of the CDM3Yn interactions was modified to account properly for both the RT and observed energy dependence of the nucleon optical potential. Based on a local density approximation, the double-folding model of the nucleus-nucleus optical potential has been extended to take into account consistently the rearrangement effect and energy dependence of the nuclear mean-field potential, using the modified CDM3Yn interactions. The extended double-folding model was applied to study the elastic $^{12}$C+$^{12}$C and $^{16}$O+$^{12}$C scattering at the refractive energies, wher...
Renormalized parameters and perturbation theory in dynamical mean-field theory for the Hubbard model
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.
Mean-field and Monte Carlo studies of the magnetization-reversal transition in the Ising model
Misra, Arkajyoti [Saha Institute of Nuclear Physics, Bidhannagar, Calcutta (India)]. E-mail: arko@cmp.saha.ernet.in; Chakrabarti, Bikas K. [Saha Institute of Nuclear Physics, Bidhannagar, Calcutta (India)]. E-mail: bikas@cmp.saha.ernet.in
2000-06-16
Detailed mean-field and Monte Carlo studies of the dynamic magnetization-reversal transition in the Ising model in its ordered phase under a competing external magnetic field of finite duration have been presented here. An approximate analytical treatment of the mean-field equations of motion shows the existence of diverging length and time scales across this dynamic transition phase boundary. These are also supported by numerical solutions of the complete mean-field equations of motion and the Monte Carlo study of the system evolving under Glauber dynamics in both two and three dimensions. Classical nucleation theory predicts different mechanisms of domain growth in two regimes marked by the strength of the external field, and the nature of the Monte Carlo phase boundary can be comprehended satisfactorily using the theory. The order of the transition changes from a continuous to a discontinuous one as one crosses over from coalescence regime (stronger field) to a nucleation regime (weaker field). Finite-size scaling theory can be applied in the coalescence regime, where the best-fit estimates of the critical exponents are obtained for two and three dimensions. (author)
State-of-the-art of beyond mean field theories with nuclear density functionals
Egido, J. Luis
2016-07-01
We present an overview of different beyond mean field theories (BMFTs) based on the generator coordinate method (GCM) and the recovery of symmetries used in many body nuclear physics with effective forces. In a first step a short reminder of the Hartree-Fock-Bogoliubov (HFB) theory is given. A general discussion of the shortcomings of any mean field approximation (MFA), stemming either from the lack of the elementary symmetries (like particle number and angular momentum) or the absence of fluctuations around the mean values, is presented. The recovery of the symmetries spontaneously broken in the HFB approach, in particular the angular momentum, is necessary, among others, to describe excited states and transitions. Particle number projection is also needed to guarantee the right number of protons and neutrons. Furthermore a projection before the variation prevents the pairing collapse in the weak pairing regime. A whole chapter is devoted to illustrate with examples the convenience of recovering symmetries and the differences between the projection before and after the variation. The lack of fluctuations around the average values of the MFA is a big shortcoming inherent to this approach. To build in correlations in BMFT one selects the relevant degrees of freedom of the atomic nucleus. In the low energy part of the spectrum these are the quadrupole, octupole and the pairing vibrations as well as the single particle degrees of freedom. In the GCM the operators representing these degrees of freedom are used as coordinates to generate, by the constrained (projected) HFB theory, a collective subspace. The highly correlated GCM wave function is finally written as a linear combination of a projected basis of this space. The variation of the coefficients of the linear combination leads to the Hill-Wheeler equation. The flexibility of the GCM Ansatz allows to describe a whole palette of physical situations by conveniently choosing the generator coordinates. We discuss the
Real-space, mean-field algorithm to numerically calculate long-range interactions
Cadilhe, A.; Costa, B. V.
2016-02-01
Long-range interactions are known to be of difficult treatment in statistical mechanics models. There are some approaches that introduce a cutoff in the interactions or make use of reaction field approaches. However, those treatments suffer the illness of being of limited use, in particular close to phase transitions. The use of open boundary conditions allows the sum of the long-range interactions over the entire system to be done, however, this approach demands a sum over all degrees of freedom in the system, which makes a numerical treatment prohibitive. Techniques like the Ewald summation or fast multipole expansion account for the exact interactions but are still limited to a few thousands of particles. In this paper we introduce a novel mean-field approach to treat long-range interactions. The method is based in the division of the system in cells. In the inner cell, that contains the particle in sight, the 'local' interactions are computed exactly, the 'far' contributions are then computed as the average over the particles inside a given cell with the particle in sight for each of the remaining cells. Using this approach, the large and small cells limits are exact. At a fixed cell size, the method also becomes exact in the limit of large lattices. We have applied the procedure to the two-dimensional anisotropic dipolar Heisenberg model. A detailed comparison between our method, the exact calculation and the cutoff radius approximation were done. Our results show that the cutoff-cell approach outperforms any cutoff radius approach as it maintains the long-range memory present in these interactions, contrary to the cutoff radius approximation. Besides that, we calculated the critical temperature and the critical behavior of the specific heat of the anisotropic Heisenberg model using our method. The results are in excellent agreement with extensive Monte Carlo simulations using Ewald summation.
Erhan Albayrak
2013-01-01
The spin-1 Blume-Capel model with transverse Ω and longitudinal external magnetic fields h,in addition to a longitudinal random crystal field D,is studied in the mean-field approximation.It is assumed that the crystal field is either turned on with probability p or turned off with probability 1-p on the sites of a square lattice.Phase diagrams are then calculated on the reduced temperature crystal field planes for given values of γ =-Ω/J and p at zero h.Thus,the effect of changing γ and p are illustrated on the phase diagrams in great detail and interesting results are observed.
Relativistic semi-classical theory of atom ionization in ultra-intense laser
无
2001-01-01
A relativistic semi-classical theory (RSCT) of H-atom ionizationin ultra-intense laser (UIL) is proposed. A relativistic analytical expression for ionization probability of H-atom in its ground state is given. This expression, compared with non-relativistic expression, clearly shows the effects of the magnet vector in the laser, the non-dipole approximation and the relativistic mass-energy relation on the ionization processes. At the same time, we show that under some conditions the relativistic expression reduces to the non-relativistic expression of non-dipole approximation. At last, some possible applications of the relativistic theory are briefly stated.
Relativistic Pseudospin Symmetry as a Supersymmetric Pattern in Nuclei
Leviatan, A
2004-01-01
Shell-model states involving several pseudospin doublets and ``intruder'' levels in nuclei, are combined into larger multiplets. The corresponding single-particle spectrum exhibits a supersymmetric pattern whose origin can be traced to the relativistic pseudospin symmetry of a nuclear mean-field Dirac Hamiltonian with scalar and vector potentials.
Special Relativistic Hydrodynamics with Gravitation
Hwang, Jai-chan; Noh, Hyerim
2016-12-01
Special relativistic hydrodynamics with weak gravity has hitherto been unknown in the literature. Whether such an asymmetric combination is possible has been unclear. Here, the hydrodynamic equations with Poisson-type gravity, considering fully relativistic velocity and pressure under the weak gravity and the action-at-a-distance limit, are consistently derived from Einstein’s theory of general relativity. An analysis is made in the maximal slicing, where the Poisson’s equation becomes much simpler than our previous study in the zero-shear gauge. Also presented is the hydrodynamic equations in the first post-Newtonian approximation, now under the general hypersurface condition. Our formulation includes the anisotropic stress.
Special relativistic hydrodynamics with gravitation
Hwang, Jai-chan
2016-01-01
The special relativistic hydrodynamics with weak gravity is hitherto unknown in the literature. Whether such an asymmetric combination is possible was unclear. Here, the hydrodynamic equations with Poisson-type gravity considering fully relativistic velocity and pressure under the weak gravity and the action-at-a-distance limit are consistently derived from Einstein's general relativity. Analysis is made in the maximal slicing where the Poisson's equation becomes much simpler than our previous study in the zero-shear gauge. Also presented is the hydrodynamic equations in the first post-Newtonian approximation, now under the {\\it general} hypersurface condition. Our formulation includes the anisotropic stress.
Relativistic magnetohydrodynamics
Hernandez, Juan; Kovtun, Pavel
2017-05-01
We present the equations of relativistic hydrodynamics coupled to dynamical electromagnetic fields, including the effects of polarization, electric fields, and the derivative expansion. We enumerate the transport coefficients at leading order in derivatives, including electrical conductivities, viscosities, and thermodynamic coefficients. We find the constraints on transport coefficients due to the positivity of entropy production, and derive the corresponding Kubo formulas. For the neutral state in a magnetic field, small fluctuations include Alfvén waves, magnetosonic waves, and the dissipative modes. For the state with a non-zero dynamical charge density in a magnetic field, plasma oscillations gap out all propagating modes, except for Alfvén-like waves with a quadratic dispersion relation. We relate the transport coefficients in the "conventional" magnetohydrodynamics (formulated using Maxwell's equations in matter) to those in the "dual" version of magnetohydrodynamics (formulated using the conserved magnetic flux).
Leardini, Fabrice
2013-01-01
This manuscript presents a problem on special relativity theory (SRT) which embodies an apparent paradox relying on the concept of simultaneity. The problem is represented in the framework of Greek epic poetry and structured in a didactic way. Owing to the characteristic properties of Lorenz transformations, three events which are simultaneous in a given inertial reference system, occur at different times in the other two reference frames. In contrast to the famous twin paradox, in the present case there are three, not two, different inertial observers. This feature provides a better framework to expose some of the main characteristics of SRT, in particular, the concept of velocity and the relativistic rule of addition of velocities.
From infinity to one: The reduction of some mean field games to a global control problem
Guéant, Olivier
2011-01-01
This paper presents recent results from Mean Field Game theory underlying the introduction of common noise that imposes to incorporate the distribution of the agents as a state variable. Starting from the usual mean field games equations introduced by J.M. Lasry and P.L. Lions and adapting them to games on graphs, we introduce a partial differential equation, often referred to as the Master equation, from which the MFG equations can be deduced. Then, this Master equation can be reinterpreted using a global control problem inducing the same behaviors as in the non-cooperative initial mean field game.
Constant entropy hybrid stars: a first approximation to cooling evolution
Mariani, M; Vucetich, H
2016-01-01
We study the possibility of a hadron-quark phase transition in the interior of neutron stars, taking into account different schematic evolutionary stages at finite temperature. We also discuss the strange quark matter stability in the quark matter phase. Furthermore, we analyze the astrophysical properties of hot and cold hybrid stars, considering the recent constraint on maximum mass given by the pulsars PSR J1614-2230 and PSR J1614-2230. We have developed a computational code to construct semi-analytical hybrid equations of state at fixed entropy per baryon to obtain different families of hybrid stars. An analytical approximation of the Field Correlator Method is used for the quark matter equation of state. For the hadronic ecuation of state, we use a table based on the relativistic mean field theory without hyperons. The phase transition is obtained imposing the Maxwell conditions, by assuming a high surface tension at the interface hadron-quark. The relativistic structure equations of hydrostatic equilibr...
Mean-field dynamos: the old concept and some recent developments
Rädler, K -H
2014-01-01
This article reproduces the Karl Schwarzschild lecture 2013. Some of the basic ideas of electrodynamics and magnetohydrodynamics of mean fields in turbulently moving conducting fluids are explained. It is stressed that the connection of the mean electromotive force with the mean magnetic field and its first spatial derivatives is in general neither local nor instantaneous and that quite a few claims concerning pretended failures of the mean-field concept result from ignoring this aspect. In addition to the mean-field dynamo mechanisms of $\\alpha^2$ and $\\alpha$ $\\Omega$ type several others are considered. Much progress in mean-field electrodynamics and magnetohydrodynamics results from the test-field method for calculating the coefficients that determine the connection of the mean electromotive force with the mean magnetic field. As an important example the memory effect in homogeneous isotropic turbulence is explained. In magnetohydrodynamic turbulence there is the possibility of a mean electromotive force t...
On the existence of classical solutions for stationary extended mean field games
Gomes, Diogo A.
2014-04-01
In this paper we consider extended stationary mean-field games, that is mean-field games which depend on the velocity field of the players. We prove various a-priori estimates which generalize the results for quasi-variational mean-field games in Gomes et al. (2012). In addition we use adjoint method techniques to obtain higher regularity bounds. Then we establish the existence of smooth solutions under fairly general conditions by applying the continuity method. When applied to standard stationary mean-field games as in Lasry and Lions (2006), Gomes and Sanchez-Morgado (2011) or Gomes et al. (2012) this paper yields various new estimates and regularity properties not available previously. We discuss additionally several examples where the existence of classical solutions can be proved. © 2013 Elsevier Ltd. All rights reserved.
Dynamical Mean-Field Theory of Electronic Correlations in Models and Materials
Vollhardt, Dieter
2010-11-01
The concept of electronic correlations plays an important role in modern condensed matter physics. It refers to interaction effects which cannot be explained within a static mean-field picture as provided by Hartree-Fock theory. Electronic correlations can have a very strong influence on the properties of materials. For example, they may turn a metal into an insulator (Mott-Hubbard metal-insulator transition). In these lecture notes I (i) introduce basic notions of the physics of correlated electronic systems, (ii) discuss the construction of mean-field theories by taking the limit of high lattice dimensions, (iii) explain the simplifications of the many-body perturbation theory in this limit which provide the basis for the formulation of a comprehensive mean-field theory for correlated fermions, the dynamical mean-field theory (DMFT), (v) derive the DMFT self-consistency equations, and (vi) apply the DMFT to investigate electronic correlations in models and materials.
On the mean-field theory of the Karlsruhe Dynamo Experiment
K.-H. Rädler
2002-01-01
Full Text Available In the Forschungszentrum Karlsruhe an experiment has been constructed which demonstrates a homogeneous dynamo as is expected to exist in the Earth's interior. This experiment is discussed within the framework of mean-field dynamo theory. The main predictions of this theory are explained and compared with the experimental results. Key words. Dynamo, geodynamo, dynamo experiment, mean-field dynamo theory, a-effect
Can realistic interaction be useful for nuclear mean-field approaches?
Nakada, H.; Sugiura, K. [Chiba University, Department of Physics, Graduate School of Science, Inage, Chiba (Japan); Inakura, T. [Chiba University, Department of Physics, Graduate School of Science, Inage, Chiba (Japan); Kyoto University, Yukawa Institute of Theoretical Physics, Sakyo, Kyoto (Japan); Niigata University, Department of Physics, Niigata (Japan); Margueron, J. [Universite de Lyon 1, CNRS/IN2P3, Institut de Physique Nucleaire de Lyon, Villeurbanne (France)
2016-07-15
Recent applications of the M3Y-type semi-realistic interaction to the nuclear mean-field approaches are presented: (i) Prediction of magic numbers and (ii) isotope shifts of nuclei with magic proton numbers. The results exemplify that the realistic interaction, which is derived from the bare 2N and 3N interaction, furnishes a new theoretical instrument for advancing nuclear mean-field approaches. (orig.)
Crowd-Averse Cyber-Physical Systems: The Paradigm of Robust Mean Field Games
Bauso, D.; Tembine, H.
2015-01-01
For a networked controlled system we illustrate the paradigm of robust mean-field games. This is a modeling framework at the interface of differential game theory, mathematical physics, and H1-optimal control that tries to capture the mutual influence between a crowd and its individuals. First, we establish a mean-field system for such games including the effects of adversarial disturbances. Second, we identify the optimal response of the individuals for a given population behavior. Third, we...
A Stochastic Maximum Principle for Risk-Sensitive Mean-Field Type Control
Djehiche, Boualem
2015-02-24
In this paper we study mean-field type control problems with risk-sensitive performance functionals. We establish a stochastic maximum principle (SMP) for optimal control of stochastic differential equations (SDEs) of mean-field type, in which the drift and the diffusion coefficients as well as the performance functional depend not only on the state and the control but also on the mean of the distribution of the state. Our result extends the risk-sensitive SMP (without mean-field coupling) of Lim and Zhou (2005), derived for feedback (or Markov) type optimal controls, to optimal control problems for non-Markovian dynamics which may be time-inconsistent in the sense that the Bellman optimality principle does not hold. In our approach to the risk-sensitive SMP, the smoothness assumption on the value-function imposed in Lim and Zhou (2005) needs not be satisfied. For a general action space a Peng\\'s type SMP is derived, specifying the necessary conditions for optimality. Two examples are carried out to illustrate the proposed risk-sensitive mean-field type SMP under linear stochastic dynamics with exponential quadratic cost function. Explicit solutions are given for both mean-field free and mean-field models.
Exact Solution Versus Gaussian Approximation for a Non-Ideal Bose Gas in One-Dimension
Tommasini, P; Natti, P L
1997-01-01
We investigate ground-state and excitation spectrum of a system of non-relativistic bosons in one-dimension interacting through repulsive, two-body contact interactions in a self-consistent Gaussian mean-field approximation which consists in writing the variationally determined density operator as the most general Gaussian functional of the quantized field operators. There are mainly two advantages in working with one-dimension. First, the existence of an exact solution for the ground-state and excitation energies. Second, neither in the perturbative results nor in the Gaussian approximation itself we do not have to deal with the three-dimensional patologies of the contact interaction . So that this scheme provides a clear comparison between these three different results. PACS numbers : 05.30.-d, 05.30.Jp, 67.40.Db
Bosonic particle-correlated states: A nonperturbative treatment beyond mean field
Jiang, Zhang; Tacla, Alexandre B.; Caves, Carlton M.
2017-08-01
Many useful properties of dilute Bose gases at ultralow temperature are predicted precisely by the (mean-field) product-state Ansatz, in which all particles are in the same quantum state. Yet, in situations where particle-particle correlations become important, the product Ansatz fails. To include correlations nonperturbatively, we consider a new set of states: the particle-correlated state of N =l ×n bosons is derived by symmetrizing the n -fold product of an l -particle quantum state. Quantum correlations of the l -particle state "spread out" to any subset of the N bosons by symmetrization. The particle-correlated states can be simulated efficiently for large N , because their parameter spaces, which depend on l , do not grow with n . Here we formulate and develop in great detail the pure-state case for l =2 , where the many-body state is constructed from a two-particle pure state. These paired wave functions, which we call pair-correlated states (PCS), were introduced by A. J. Leggett [Rev. Mod. Phys. 73, 307 (2001), 10.1103/RevModPhys.73.307] as a particle-number-conserving version of the Bogoliubov approximation. We present an iterative algorithm that solves for the reduced (marginal) density matrices (RDMs), i.e., the correlation functions, associated with PCS in time O (N ) . The RDMs can also be derived from the normalization factor of PCS, which is derived analytically in the large-N limit. To test the efficacy of PCS, we analyze the ground state of the two-site Bose-Hubbard model by minimizing the energy of the PCS state, both in its exact form and in its large-N approximate form, and comparing with the exact ground state. For N =1000 , the relative errors of the ground-state energy for both cases are within 10-5 over the entire parameter region from a single condensate to a Mott insulator. We present numerical results that suggest that PCS might be useful for describing the dynamics in the strongly interacting regime.
Yamamoto, Takeshi
2008-12-01
Conventional quantum chemical solvation theories are based on the mean-field embedding approximation. That is, the electronic wavefunction is calculated in the presence of the mean field of the environment. In this paper a direct quantum mechanical/molecular mechanical (QM/MM) analog of such a mean-field theory is formulated based on variational and perturbative frameworks. In the variational framework, an appropriate QM/MM free energy functional is defined and is minimized in terms of the trial wavefunction that best approximates the true QM wavefunction in a statistically averaged sense. Analytical free energy gradient is obtained, which takes the form of the gradient of effective QM energy calculated in the averaged MM potential. In the perturbative framework, the above variational procedure is shown to be equivalent to the first-order expansion of the QM energy (in the exact free energy expression) about the self-consistent reference field. This helps understand the relation between the variational procedure and the exact QM/MM free energy as well as existing QM/MM theories. Based on this, several ways are discussed for evaluating non-mean-field effects (i.e., statistical fluctuations of the QM wavefunction) that are neglected in the mean-field calculation. As an illustration, the method is applied to an SN2 Menshutkin reaction in water, NH3+CH3Cl→NH3CH3++Cl-, for which free energy profiles are obtained at the Hartree-Fock, MP2, B3LYP, and BHHLYP levels by integrating the free energy gradient. Non-mean-field effects are evaluated to be reaction in water.
Asymmetric Neutrino Reaction in Magnetized Proto-Neutron Stars in Fully Relativistic Approach
Yasutake Nobutoshi
2012-02-01
Full Text Available We calculate asymmetric neutrino absorption and scattering cross sections on hot and dense magnetized neutron-star matter including hyperons in fully relativistic mean-field theory. The absorption/scattering cross sections are suppressed/enhanced incoherently in the direction of the magnetic field B = Bẑ. The asymmetry is 2–4% at the matter density ρ0 ≤ ρB ≤ 3ρ0 and temperature T ≤ 40MeV for B = 2 × 1017G. Then we solve the Boltzmann equation for the neutrino transport in 1D attenuation approximation, and get the result that the kick velocity becomes about 300 km/s for the proto-neutron star with 168 solar mass at T = 20MeV.
Finite-size and correlation-induced effects in Mean-field Dynamics
Touboul, Jonathan
2010-01-01
The brain's activity is characterized by the interaction of a very large number of neurons that are strongly affected by noise. However, signals often arise at macroscopic scales integrating the effect of many neurons into a reliable pattern of activity. In order to study such large neuronal assemblies, one is often led to derive mean-field limits summarizing the effect of the interaction of a large number of neurons into an effective signal. Classical mean-field approaches consider the evolution of a deterministic variable, the mean activity, thus neglecting the stochastic nature of neural behavior. In this article, we build upon a recent approach that includes correlations and higher order moments in mean-field equations, and study how these stochastic effects influence the solutions of the mean-field equations, both in the limit of an infinite number of neurons and for large yet finite networks. We show that, though the solutions of the deterministic mean-field equation constitute uncorrelated solutions of...
Rädler, K.-H.
This article elucidates the basic ideas of electrodynamics and magnetohydrodynamics of mean fields in turbulently moving conducting fluids. It is stressed that the connection of the mean electromotive force with the mean magnetic field and its first spatial derivatives is in general neither local nor instantaneous and that quite a few claims concerning pretended failures of the mean-field concept result from ignoring this aspect. In addition to the mean-field dynamo mechanisms of α2 and α Ω type several others are considered. Much progress in mean-field electrodynamics and magnetohydrodynamics results from the test-field method for calculating the coefficients that determine the connection of the mean electromotive force with the mean magnetic field. As an important example the memory effect in homogeneous isotropic turbulence is explained. In magnetohydrodynamic turbulence there is the possibility of a mean electromotive force that is primarily independent of the mean magnetic field and labeled as Yoshizawa effect. Despite of many efforts there is so far no convincing comprehensive theory of α quenching, that is, the reduction of the α effect with growing mean magnetic field, and of the saturation of mean-field dynamos. Steps toward such a theory are explained. Finally, some remarks on laboratory experiments with dynamos are made.
Komissarov, S S; Lyutikov, M
2015-01-01
In this paper we describe a simple numerical approach which allows to study the structure of steady-state axisymmetric relativistic jets using one-dimensional time-dependent simulations. It is based on the fact that for narrow jets with v~c the steady-state equations of relativistic magnetohydrodynamics can be accurately approximated by the one-dimensional time-dependent equations after the substitution z=ct. Since only the time-dependent codes are now publicly available this is a valuable and efficient alternative to the development of a high-specialized code for the time-independent equations. The approach is also much cheaper and more robust compared to the relaxation method. We tested this technique against numerical and analytical solutions found in literature as well as solutions we obtained using the relaxation method and found it sufficiently accurate. In the process, we discovered the reason for the failure of the self-similar analytical model of the jet reconfinement in relatively flat atmospheres a...
Relativistic diffusive motion in random electromagnetic fields
Haba, Z, E-mail: zhab@ift.uni.wroc.pl [Institute of Theoretical Physics, University of Wroclaw, 50-204 Wroclaw, Plac Maxa Borna 9 (Poland)
2011-08-19
We show that the relativistic dynamics in a Gaussian random electromagnetic field can be approximated by the relativistic diffusion of Schay and Dudley. Lorentz invariant dynamics in the proper time leads to the diffusion in the proper time. The dynamics in the laboratory time gives the diffusive transport equation corresponding to the Juettner equilibrium at the inverse temperature {beta}{sup -1} = mc{sup 2}. The diffusion constant is expressed by the field strength correlation function (Kubo's formula).
Lerchner, A; Hertz, J; Ahmadi, M
2004-01-01
We present a complete mean field theory for a balanced state of a simple model of an orientation hypercolumn. The theory is complemented by a description of a numerical procedure for solving the mean-field equations quantitatively. With our treatment, we can determine self-consistently both the firing rates and the firing correlations, without being restricted to specific neuron models. Here, we solve the analytically derived mean-field equations numerically for integrate-and-fire neurons. Several known key properties of orientation selective cortical neurons emerge naturally from the description: Irregular firing with statistics close to -- but not restricted to -- Poisson statistics; an almost linear gain function (firing frequency as a function of stimulus contrast) of the neurons within the network; and a contrast-invariant tuning width of the neuronal firing. We find that the irregularity in firing depends sensitively on synaptic strengths. If Fano factors are bigger than 1, then they are so for all stim...
Exact mean field dynamics for epidemic-like processes on heterogeneous networks
Lucas, Andrew
2012-01-01
We show that the mean field equations for the SIR epidemic can be exactly solved for a network with arbitrary degree distribution. Our exact solution consists of reducing the dynamics to a lone first order differential equation, which has a solution in terms of an integral over functions dependent on the degree distribution of the network, and reconstructing all mean field functions of interest from this integral. Irreversibility of the SIR epidemic is crucial for the solution. We also find exact solutions to the sexually transmitted disease SI epidemic on bipartite graphs, to a simplified rumor spreading model, and to a new model for recommendation spreading, via similar techniques. Numerical simulations of these processes on scale free networks demonstrate the qualitative validity of mean field theory in most regimes.
Mean-Field Backward Stochastic Evolution Equations in Hilbert Spaces and Optimal Control for BSPDEs
Ruimin Xu
2014-01-01
Full Text Available We obtain the existence and uniqueness result of the mild solutions to mean-field backward stochastic evolution equations (BSEEs in Hilbert spaces under a weaker condition than the Lipschitz one. As an intermediate step, the existence and uniqueness result for the mild solutions of mean-field BSEEs under Lipschitz condition is also established. And then a maximum principle for optimal control problems governed by backward stochastic partial differential equations (BSPDEs of mean-field type is presented. In this control system, the control domain need not to be convex and the coefficients, both in the state equation and in the cost functional, depend on the law of the BSPDE as well as the state and the control. Finally, a linear-quadratic optimal control problem is given to explain our theoretical results.
Relativistic description of electron scattering on the deuteron
Hummel, E
1994-01-01
Within a quasipotential framework a relativistic analysis is presented of the deuteron current. Assuming that the singularities from the nucleon propagators are important, a so-called equal time approximation of the current is constructed. This is applied to both elastic and inelastic electron scattering. As dynamical model the relativistic one boson exchange model is used. Reasonable agreement is found with a previous relativistic calculation of the elastic electromagnetic form factors of the deuteron. For the unpolarized inelastic electron scattering effects of final state interactions and relativistic corrections to the structure functions are considered in the impulse approximation. Two specific kinematic situations are studied as examples.
Mean-field theory of globally coupled integrate-and-fire neural oscillators with dynamic synapses
Bressloff, P. C.
1999-08-01
We analyze the effects of synaptic depression or facilitation on the existence and stability of the splay or asynchronous state in a population of all-to-all, pulse-coupled neural oscillators. We use mean-field techniques to derive conditions for the local stability of the splay state and determine how stability depends on the degree of synaptic depression or facilitation. We also consider the effects of noise. Extensions of the mean-field results to finite networks are developed in terms of the nonlinear firing time map.
Another mean field treatment in the strong coupling limit of lattice QCD
Ohnishi, Akira; Miura, Kohtaroh; Nakano, Takashi Z.
2011-01-01
We discuss the QCD phase diagram in the strong coupling limit of lattice QCD by using a new type of mean field coming from the next-to-leading order of the large dimensional expansion. The QCD phase diagram in the strong coupling limit recently obtained by using the monomer-dimer-polymer (MDP) algorithm has some differences in the phase boundary shape from that in the mean field results. As one of the origin to explain the difference, we consider another type of auxiliary field, which corresp...
Skyrme mean-field studies of nuclei far from the stability line
Heenen, P H; Cwiok, S; Nazarewicz, W; Valor, A
1999-01-01
Two applications of mean-field calculations based on 3D coordinate-space techniques are presented. The first concerns the structure of odd-N superheavy elements that have been recently observed experimentally and shows the ability of the method to describe, in a self-consistent way, very heavy odd-mass nuclei. Our results are consistent with the experimental data. The second application concerns the introduction of correlations beyond a mean-field approach by means of projection techniques and configuration mixing. Results for Mg isotopes demonstrate that the restoration of rotational symmetry plays a crucial role in the description of 32Mg.
Dynamical mean field theory-based electronic structure calculations for correlated materials.
Biermann, Silke
2014-01-01
We give an introduction to dynamical mean field approaches to correlated materials. Starting from the concept of electronic correlation, we explain why a theoretical description of correlations in spectroscopic properties needs to go beyond the single-particle picture of band theory.We discuss the main ideas of dynamical mean field theory and its use within realistic electronic structure calculations, illustrated by examples of transition metals, transition metal oxides, and rare-earth compounds. Finally, we summarise recent progress on the calculation of effective Hubbard interactions and the description of dynamical screening effects in solids.
Time-Dependent Mean-Field Games in the Subquadratic Case
Gomes, Diogo A.
2014-10-14
In this paper we consider time-dependent mean-field games with subquadratic Hamiltonians and power-like local dependence on the measure. We establish existence of classical solutions under a certain set of conditions depending on both the growth of the Hamiltonian and the dimension. This is done by combining regularity estimates for the Hamilton-Jacobi equation based on the Gagliardo-Nirenberg interpolation inequality with polynomial estimates for the Fokker-Planck equation. This technique improves substantially the previous results on the regularity of time-dependent mean-field games.
On the convergence of finite state mean-field games through Γ-convergence
Ferreira, Rita C.
2014-10-01
In this study, we consider the long-term convergence (trend toward an equilibrium) of finite state mean-field games using Γ-convergence. Our techniques are based on the observation that an important class of mean-field games can be viewed as the Euler-Lagrange equation of a suitable functional. Therefore, using a scaling argument, one can convert a long-term convergence problem into a Γ-convergence problem. Our results generalize previous results related to long-term convergence for finite state problems. © 2014 Elsevier Inc.
Non-mean-field effects in systems with long-range forces in competition.
Bachelard, R; Staniscia, F
2012-11-01
We investigate the canonical equilibrium of systems with long-range forces in competition. These forces create a modulation in the interaction potential and modulated phases appear at the system scale. The structure of these phases differentiate this system from monotonic potentials, where only the mean-field and disordered phases exist. With increasing temperature, the system switches from one ordered phase to another through a first-order phase transition. Both mean-field and modulated phases may be stable, even at zero temperature, and the long-range nature of the interaction will lead to metastability characterized by extremely long time scales.
Wilten eNicola
2016-02-01
Full Text Available A fundamental question in computational neuroscience is how to connect a network of spiking neurons to produce desired macroscopic or mean field dynamics. One possible approach is through the Neural Engineering Framework (NEF. The NEF approach requires quantities called decoders which are solved through an optimization problem requiring large matrix inversion. Here, we show how a decoder can be obtained analytically for type I and certain type II firing rates as a function of the heterogeneity of its associated neuron. These decoders generate approximants for functions that converge to the desired function in mean-squared error like 1/N, where N is the number of neurons in the network. We refer to these decoders as scale-invariant decoders due to their structure. These decoders generate weights for a network of neurons through the NEF formula for weights. These weights force the spiking network to have arbitrary and prescribed mean field dynamics. The weights generated with scale-invariant decoders all lie on low dimensional hypersurfaces asymptotically. We demonstrate the applicability of these scale-invariant decoders and weight surfaces by constructing networks of spiking theta neurons that replicate the dynamics of various well known dynamical systems such as the neural integrator, Van der Pol system and the Lorenz system. As these decoders are analytically determined and non-unique, the weights are also analytically determined and non-unique. We discuss the implications for measured weights of neuronal networks
Relativistic Fractal Cosmologies
Ribeiro, Marcelo B
2009-01-01
This article reviews an approach for constructing a simple relativistic fractal cosmology whose main aim is to model the observed inhomogeneities of the distribution of galaxies by means of the Lemaitre-Tolman solution of Einstein's field equations for spherically symmetric dust in comoving coordinates. This model is based on earlier works developed by L. Pietronero and J.R. Wertz on Newtonian cosmology, whose main points are discussed. Observational relations in this spacetime are presented, together with a strategy for finding numerical solutions which approximate an averaged and smoothed out single fractal structure in the past light cone. Such fractal solutions are shown, with one of them being in agreement with some basic observational constraints, including the decay of the average density with the distance as a power law (the de Vaucouleurs' density power law) and the fractal dimension in the range 1 <= D <= 2. The spatially homogeneous Friedmann model is discussed as a special case of the Lemait...
Cattaneo, Carlo
2011-01-01
This title includes: Pham Mau Quam: Problemes mathematiques en hydrodynamique relativiste; A. Lichnerowicz: Ondes de choc, ondes infinitesimales et rayons en hydrodynamique et magnetohydrodynamique relativistes; A.H. Taub: Variational principles in general relativity; J. Ehlers: General relativistic kinetic theory of gases; K. Marathe: Abstract Minkowski spaces as fibre bundles; and, G. Boillat: Sur la propagation de la chaleur en relativite.
Test of Relativistic Eigenfunctions for Pseudospin Symmetry
Ginocchio, Joseph N.
2001-10-01
Pseudospin symmetry has been shown to be a relativistic symmetry of the Dirac Hamiltonian [1] and the generators of this symmetry have been determined [2]. Although the measured energy splittings between pseudospin doublets are small, the eigenfunctions of the doublets have been examined only recently [3]. We show to what extent the pseudospin partners of realistic relativistic mean field eigenfunctions [4] are themselves eigenfunctions of the same Dirac Hamiltonian. 1) J. N. Ginocchio, Phys. Rev. Lett. 78, 436 (1997). 2) J. N. Ginocchio and A. Leviatan, Phys. Lett. B 425, 1 (1998). 3) J. N. Ginocchio and A. Leviatan, to be published in Phys. Rev. Lett. (2001). 4) J. N. Ginocchio and D. G. Madland, Phys. Rev. C 57, 1167 (1998).
A Two-Mode Mean-Field Optimal Switching Problem for the Full Balance Sheet
Boualem Djehiche
2014-01-01
a two-mode optimal switching problem of mean-field type, which can be described by a system of Snell envelopes where the obstacles are interconnected and nonlinear. The main result of the paper is a proof of a continuous minimal solution to the system of Snell envelopes, as well as the full characterization of the optimal switching strategy.
Another mean field treatment in the strong coupling limit of lattice QCD
Ohnishi, Akira; Nakano, Takashi Z
2010-01-01
We discuss the QCD phase diagram in the strong coupling limit of lattice QCD by using a new type of mean field coming from the next-to-leading order of the large dimensional expansion. The QCD phase diagram in the strong coupling limit recently obtained by using the monomer-dimer-polymer (MDP) algorithm has some differences in the phase boundary shape from that in the mean field results. As one of the origin to explain the difference, we consider another type of auxiliary field, which corresponds to the point-splitting mesonic composite. Fermion determinant with this mean field under the anti-periodic boundary condition gives rise to a term which interpolates the effective potentials in the previously proposed zero and finite temperature mean field treatments. While the shift of the transition temperature at zero chemical potential is in the desirable direction and the phase boundary shape is improved, we find that the effects are too large to be compatible with the MDP simulation results.
Mean Field Theory, Ginzburg Criterion, and Marginal Dimensionality of Phase-Transitions
Als-Nielsen, Jens Aage; Birgenau, R. J.
1977-01-01
By applying a real space version of the Ginzburg criterion, the role of fluctuations and thence the self‐consistency of mean field theory are assessed in a simple fashion for a variety of phase transitions. It is shown that in using this approach the concept of ’’marginal dimensionality’’ emerges...
Explicit solutions of one-dimensional, first-order, stationary mean-field games with congestion
Gomes, Diogo A.
2017-01-05
Here, we consider one-dimensional first-order stationary mean-field games with congestion. These games arise when crowds face difficulty moving in high-density regions. We look at both monotone decreasing and increasing interactions and construct explicit solutions using the current formulation. We observe new phenomena such as discontinuities, unhappiness traps and the non-existence of solutions.
Phase behaviour of colloids suspended in a near-critical solvent : A mean-field approach
Edison, John R.; Belli, Simone; Evans, Robert; Van Roij, René; Dijkstra, Marjolein
2015-01-01
Colloids suspended in a binary solvent may, under suitable thermodynamic conditions, experience a wide variety of solvent-mediated interactions that can lead to colloidal phase transitions and aggregation phenomena. We present a simple mean-field theory, based on free-volume arguments, that describe
Going Beyond a Mean-field Model for the Learning Cortex: Second-Order Statistics
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
Iacobelli, Giulio; Kuelske, Christof
We consider a general class of disordered mean-field models where both the spin variables and disorder variables eta take finitely many values. To investigate the size-dependence in the phase-transition regime we construct the metastate describing the probabilities to find a large system close to a
Mean-field description of the structure and tension of curved fluid interfaces
Kuipers, Joris
2009-01-01
This thesis described the interfacial properties of curved fluid interfaces mainly employing mean-field models. Investigations of Tolman's length in simple systems and systems in contact with a hard wall are presented. Both the interfacial properties as well as the wetting behavior of phase-separate
Ground state correlations and mean field using the exp(S) method
Heisenberg, J H; Heisenberg, Jochen H.; Mihaila, Bogdan
1999-01-01
This document gives a detailed account of the terms used in the computation of the ground state mean field and the ground state correlations. While the general approach to this description is given in a separate paper (nucl-th/9802029) we give here the explicite expressions used.
Automating the mean-field method for large dynamic gossip networks
Bakhshi, Rena; Endrullis, Jörg; Endrullis, Stefan; Fokkink, Wan; Haverkort, Boudewijn
2010-01-01
We investigate an abstraction method, called mean- field method, for the performance evaluation of dynamic net- works with pairwise communication between nodes. It allows us to evaluate systems with very large numbers of nodes, that is, systems of a size where traditional performance evaluation meth
New a priori estimates for mean-field games with congestion
Evangelista, David
2016-01-06
We present recent developments in crowd dynamics models (e.g. pedestrian flow problems). Our formulation is given by a mean-field game (MFG) with congestion. We start by reviewing earlier models and results. Next, we develop our model. We establish new a priori estimates that give partial regularity of the solutions. Finally, we discuss numerical results.
Mean field limit for bosons and infinite dimensional phase-space analysis
Zied, Ammari
2007-01-01
This article proposes the construction of Wigner measures in the infinite dimensional bosonic quantum field theory, with applications to the derivation of the mean field dynamics. Once these asymptotic objects are well defined, it is shown how they can be used to make connections between different kinds of results or to prove new ones.
Mott-Hubbard and Anderson transitions in dynamical mean-field theory
Byczuk, Krzysztof [Institute of Theoretical Physics, Warsaw University, ul. Hoza 69, PL-00-681 Warsaw (Poland)]. E-mail: byczuk@fuw.edu.pl; Hofstetter, Walter [Condensed Matter Theory Group, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Vollhardt, Dieter [Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute for Physics, University of Augsburg, D-86135 Augsburg (Germany)
2005-04-30
The Anderson-Hubbard Hamiltonian at half-filling is investigated within dynamical mean-field theory at zero temperature. The local density of states is calculated by taking the geometric and arithmetic mean, respectively. The non-magnetic ground state phase diagrams obtained within the different averaging schemes are compared.
Mean-field cosmological dynamos in Riemannian space with isotropic diffusion
de Andrade, L Garcia
2009-01-01
Mean-field cosmological dynamos in Riemannian space with isotropic diffusion}} Previous attempts for building a cosmic dynamo including preheating in inflationary universes [Bassett et al Phys Rev (2001)] has not included mean field or turbulent dynamos. In this paper a mean field dynamo in cosmic scales on a Riemannian spatial cosmological section background, is set up. When magnetic fields and flow velocities are parallel propagated along the Riemannian space dynamo action is obtained. Turbulent diffusivity ${\\beta}$ is coupled with the Ricci magnetic curvature, as in Marklund and Clarkson [MNRAS (2005)], GR-MHD dynamo equation. Mean electric field possesses an extra term where Ricci tensor couples with magnetic vector potential in Ohm's law. In Goedel universe induces a mean field dynamo growth rate ${\\gamma}=2{\\omega}^{2}{\\beta}$. In this frame kinetic helicity vanishes. In radiation era this yields ${\\gamma}\\approx{2{\\beta}{\\times}10^{-12}s^{-1}}$. In non-comoving the magnetic field is expressed as $B\\ap...
Abaimov, Sergey G.; Akhatov, Iskander S.
2016-09-01
In this study, we apply the mean-field approach to the three-dimensional damage phenomena. The model approximates a solid as a polycrystalline material where grains are assumed isotropic. While the stiffness properties are considered homogeneous, the heterogeneous distribution of grains' strengths provides the quenched statistical variability generating non-thermal fluctuations in the ensemble. Studying the statistical properties of the fluctuations, we introduce the concept of susceptibility of damage. Its divergence in the vicinity of the point of material failure can be treated as a catastrophe predictor. In accordance with this criterion, we find that damage growth in reality is much faster than it could be expected from intuitive engineering considerations. Also, we consider avalanches of grain failures and find that due to the slowing down effect the characteristic time of the relaxation processes diverges in the vicinity of the point of material failure.
Gukelberger, Jan; Hafermann, Hartmut
2016-01-01
The dual-fermion approach provides a formally exact prescription for calculating properties of a correlated electron system in terms of a diagrammatic expansion around dynamical mean-field theory (DMFT). It can address the full range of interactions, the lowest order theory is asymptotically exact in both the weak- and strong-coupling limits, and the technique naturally incorporates long-range correlations beyond the reach of current cluster extensions to DMFT. Most practical implementations, however, neglect higher-order interaction vertices beyond two-particle scattering in the dual effective action and further truncate the diagrammatic expansion in the two-particle scattering vertex to a leading-order or ladder-type approximation. In this work we compute the dual-fermion expansion for the Hubbard model including all diagram topologies with two-particle interactions to high orders by means of a stochastic diagrammatic Monte Carlo algorithm. We use benchmarking against numerically exact Diagrammatic Determin...
Finite-State Mean-Field Games, Crowd Motion Problems, and its Numerical Methods
Machado Velho, Roberto
2017-09-10
In this dissertation, we present two research projects, namely finite-state mean-field games and the Hughes model for the motion of crowds. In the first part, we describe finite-state mean-field games and some applications to socio-economic sciences. Examples include paradigm shifts in the scientific community and the consumer choice behavior in a free market. The corresponding finite-state mean-field game models are hyperbolic systems of partial differential equations, for which we propose and validate a new numerical method. Next, we consider the dual formulation to two-state mean-field games, and we discuss numerical methods for these problems. We then depict different computational experiments, exhibiting a variety of behaviors, including shock formation, lack of invertibility, and monotonicity loss. We conclude the first part of this dissertation with an investigation of the shock structure for two-state problems. In the second part, we consider a model for the movement of crowds proposed by R. Hughes in [56] and describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an Eikonal equation with Dirichlet or Neumann data. We first establish a priori estimates for the solutions. Next, we consider radial solutions, and we identify a shock formation mechanism. Subsequently, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. We also propose a new numerical method for the solution of Fokker-Planck equations and then to systems of PDEs composed by a Fokker-Planck equation and a potential type equation. Finally, we illustrate the use of the numerical method both to the Hughes model and mean-field games. We also depict cases such as the evacuation of a room and the movement of persons around Kaaba (Saudi Arabia).
Relativistic radiative transfer in relativistic spherical flows
Fukue, Jun
2017-02-01
Relativistic radiative transfer in relativistic spherical flows is numerically examined under the fully special relativistic treatment. We first derive relativistic formal solutions for the relativistic radiative transfer equation in relativistic spherical flows. We then iteratively solve the relativistic radiative transfer equation, using an impact parameter method/tangent ray method, and obtain specific intensities in the inertial and comoving frames, as well as moment quantities, and the Eddington factor. We consider several cases; a scattering wind with a luminous central core, an isothermal wind without a core, a scattering accretion on to a luminous core, and an adiabatic accretion on to a dark core. In the typical wind case with a luminous core, the emergent intensity is enhanced at the center due to the Doppler boost, while it reduces at the outskirts due to the transverse Doppler effect. In contrast to the plane-parallel case, the behavior of the Eddington factor is rather complicated in each case, since the Eddington factor depends on the optical depth, the flow velocity, and other parameters.
Skyrme's interaction beyond the mean-field. The DGCM+GOA Hamiltonian of nuclear quadrupole motion
Kluepfel, Peter
2008-07-29
This work focuses on the microscopic description of nuclear collective quadrupole motion within the framework of the dynamic Generator-Coordinate-Method(DGCM)+Gaussian-Overlap-Approximation(GOA). Skyrme-type effective interactions are used as the fundamental many-particle interaction. Starting from a rotational invariant, polynomial and topologic consistent formulation of the GCM+GOA Hamiltonian an interpolation scheme for the collective masses and potential is developed. It allows to define the collective Hamiltonian of fully triaxial collective quadrupole dynamics from a purely axial symmetric configuration space. The substantial gain in performance allows the self-consistent evaluation of the dynamic quadrupole mass within the ATDHF-cranking model. This work presents the first large-scale analysis of quadrupole correlation energies and lowlying collective states within the DGCM+GOA model. Different Skyrme- and pairing interactions are compared from old standards up to more recent parameterizations. After checking the validity of several approximations to the DGCM+GOA model - both on the mean-field and the collective level - we proceed with a detailed investigation of correlation effects along the chains of semi-magic isotopes and isotones. This finally allows to define a set of observables which are hardly affected by collective correlations. Those observables were used for a refit of a Skyrme-type effective interaction which is expected to cure most of the problems of the recent parameterizations. Preparing further work, estimates for the correlated ground state energy are proposed which can be evaluated directly from the mean-field model. (orig.)
On the relativistic mass function and averaging in cosmology
Ostrowski, Jan J; Roukema, Boudewijn F
2016-01-01
The general relativistic description of cosmological structure formation is an important challenge from both the theoretical and the numerical point of views. In this paper we present a brief prescription for a general relativistic treatment of structure formation and a resulting mass function on galaxy cluster scales in a highly generic scenario. To obtain this we use an exact scalar averaging scheme together with the relativistic generalization of Zel'dovich's approximation (RZA) that serves as a closure condition for the averaged equations.
Merino-Aceituno, Sara
2016-12-01
The isotropic 4-wave kinetic equation is considered in its weak formulation using model (simplified) homogeneous kernels. Existence and uniqueness of solutions is proven in a particular setting where the kernels have a rate of growth at most linear. We also consider finite stochastic particle systems undergoing instantaneous coagulation-fragmentation phenomena and give conditions in which this system approximates the solution of the equation (mean-field limit).
General relativistic corrections and non-Gaussianity
Villa, Eleonora; Matarrese, Sabino
2014-01-01
General relativistic cosmology cannot be reduced to linear relativistic perturbations superposed on an isotropic and homogeneous (Friedmann-Robertson-Walker) background, even though such a simple scheme has been successfully applied to analyse a large variety of phenomena (such as Cosmic Microwave Background primary anisotropies, matter clustering on large scales, weak gravitational lensing, etc.). The general idea of going beyond this simple paradigm is what characterises most of the efforts made in recent years: the study of second and higher-order cosmological perturbations including all general relativistic contributions -- also in connection with primordial non-Gaussianities -- the idea of defining large-scale structure observables directly from a general relativistic perspective, the various attempts to go beyond the Newtonian approximation in the study of non-linear gravitational dynamics, by using e.g., Post-Newtonian treatments, are all examples of this general trend. Here we summarise some of these ...
Relativistic calculations of coalescing binary neutron stars
Joshua Faber; Phillippe Grandclément; Frederic Rasio
2004-10-01
We have designed and tested a new relativistic Lagrangian hydrodynamics code, which treats gravity in the conformally flat approximation to general relativity. We have tested the resulting code extensively, finding that it performs well for calculations of equilibrium single-star models, collapsing relativistic dust clouds, and quasi-circular orbits of equilibrium solutions. By adding a radiation reaction treatment, we compute the full evolution of a coalescing binary neutron star system. We find that the amount of mass ejected from the system, much less than a per cent, is greatly reduced by the inclusion of relativistic gravitation. The gravity wave energy spectrum shows a clear divergence away from the Newtonian point-mass form, consistent with the form derived from relativistic quasi-equilibrium fluid sequences.
Energy spectra in relativistic electron precipitation events.
Rosenberg, T. J.; Lanzerotti, L. J.; Bailey, D. K.; Pierson, J. D.
1972-01-01
Two events in August 1967, categorized as relativistic electron precipitation (REP) events by their effect on VHF transmissions propagated via the forward-scatter mode, have been examined with regard to the energy spectra of trapped and precipitated electrons. These two substorm-associated events August 11 and August 25 differ with respect to the relativistic, trapped electron population at synchronous altitude; in the August 25 event there was a nonadiabatic enhancement of relativistic (greater than 400 keV) electrons, while in the August 11 event no relativistic electrons were produced. In both events electron spectra deduced from bremsstrahlung measurements (made on a field line close to that of the satellite) had approximately the same e-folding energies as the trapped electron enhancements. However, the spectrum of electrons in the August 25 event was significantly harder than the spectrum in the event of August 11.
Backes, Steffen
2017-04-15
The study of the electronic properties of correlated systems is a very diverse field and has lead to valuable insight into the physics of real materials. In these systems, the decisive factor that governs the physical properties is the ratio between the electronic kinetic energy, which promotes delocalization over the lattice, and the Coulomb interaction, which instead favours localized electronic states. Due to this competition, correlated electronic systems can show unique and interesting properties like the Metal-Insulator transition, diverse phase diagrams, strong temperature dependence and in general a high sensitivity to the environmental conditions. A theoretical description of these systems is not an easy task, since perturbative approaches that do not preserve the competition between the kinetic and interaction terms can only be applied in special limiting cases. One of the most famous approaches to obtain the electronic properties of a real material is the ab initio density functional theory (DFT) method. It allows one to obtain the ground state density of the system under investigation by mapping onto an effective non-interacting system that has to be found self-consistently. While being an exact theory, in practical implementations certain approximations have to be made to the exchange-correlation potential. The local density approximation (LDA), which approximates the exchange-correlation contribution to the total energy by that of a homogeneous electron gas with the corresponding density, has proven quite successful in many cases. Though, this approximation in general leads to an underestimation of electronic correlations and is not able to describe a metal-insulator transition due to electronic localization in the presence of strong Coulomb interaction. A different approach to the interacting electronic problem is the dynamical mean-field theory (DMFT), which is non-perturbative in the kinetic and interaction term but neglects all non
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.
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.
Relativistic Remnants of Non-Relativistic Electrons
Kashiwa, Taro
2015-01-01
Electrons obeying the Dirac equation are investigated under the non-relativistic $c \\mapsto \\infty$ limit. General solutions are given by derivatives of the relativistic invariant functions whose forms are different in the time- and the space-like region, yielding the delta function of $(ct)^2 - x^2$. This light-cone singularity does survive to show that the charge and the current density of electrons travel with the speed of light in spite of their massiveness.
Asynchronous stochastic approximation with differential inclusions
David S. Leslie
2012-01-01
Full Text Available The asymptotic pseudo-trajectory approach to stochastic approximation of Benaïm, Hofbauer and Sorin is extended for asynchronous stochastic approximations with a set-valued mean field. The asynchronicity of the process is incorporated into the mean field to produce convergence results which remain similar to those of an equivalent synchronous process. In addition, this allows many of the restrictive assumptions previously associated with asynchronous stochastic approximation to be removed. The framework is extended for a coupled asynchronous stochastic approximation process with set-valued mean fields. Two-timescales arguments are used here in a similar manner to the original work in this area by Borkar. The applicability of this approach is demonstrated through learning in a Markov decision process.
Beyond the mean field in the particle-vibration coupling scheme
Baldo, M; Colo', G; Rizzo, D; Sciacchitano, L
2015-01-01
The Energy Density Functional theory is one of the most used methods developed in nuclear structure. It is based on the assumption that the energy of the ground state is a functional only of the density profile. The method is extremely successful within the effective force approach, noticeably the Skyrme or Gogny forces, in reproducing the nuclear binding energies and other bulk properties along the whole mass table. Although the Density Functional is in this case represented formally as the Hartree-Fock mean field of an effective force, the corresponding single-particle states in general do not reproduce the phenomenology particularly well. To overcome this difficulty, a strategy has been developed where the effective force is adjusted to reproduce directly the single particle energies, trying to keep the ground state energy sufficiently well reproduced. An alternative route, that has been developed along several years, for solving this problem is to introduce the mean field fluctuations, as represented by t...
Mean field theory for Lyapunov exponents and KS entropy in Lorentz lattice gases
Ernst, M H; Nix, R; Jacobs, D; Ernst, M H; Dorfman, J R; Nix, R; Jacobs, D
1994-01-01
automata lattice gases are useful systems for systematically exploring the connections between non-equilibrium statistical mechanics and dynamical systems theory. Here the chaotic properties of a Lorentz lattice gas are studied analytically and by means of computer simulations. The escape-rates, Lyapunov exponents, and KS entropies are estimated for a one- dimensional example using a mean field theory. The results are compared with simulations for a range of densities and scattering parameters of the lattice gas. The computer results show a distribution of values for the dynamical quantities with average values that are in good agreement with the mean field theory and consistent with the escape-rate formalism for the coefficient of diffusion.
Mean-Field Limit and Phase Transitions for Nematic Liquid Crystals in the Continuum
Bachmann, Sven; Genoud, François
2017-08-01
We discuss thermotropic nematic liquid crystals in the mean-field regime. In the first part of this article, we rigorously carry out the mean-field limit of a system of N rod-like particles as N→ ∞, which yields an effective `one-body' free energy functional. In the second part, we focus on spatially homogeneous systems, for which we study the associated Euler-Lagrange equation, with a focus on phase transitions for general axisymmetric potentials. We prove that the system is isotropic at high temperature, while anisotropic distributions appear through a transcritical bifurcation as the temperature is lowered. Finally, as the temperature goes to zero we also prove, in the concrete case of the Maier-Saupe potential, that the system converges to perfect nematic order.
Mean-field analysis of phase transitions in the emergence of hierarchical society
Okubo, Tsuyoshi; Odagaki, Takashi
2007-09-01
Emergence of hierarchical society is analyzed by use of a simple agent-based model. We extend the mean-field model of Bonabeau [Physica A 217, 373 (1995)] to societies obeying complex diffusion rules where each individual selects a moving direction following their power rankings. We apply this mean-field analysis to the pacifist society model recently investigated by use of Monte Carlo simulation [Physica A 367, 435 (2006)]. We show analytically that the self-organization of hierarchies occurs in two steps as the individual density is increased and there are three phases: one egalitarian and two hierarchical states. We also highlight that the transition from the egalitarian phase to the first hierarchical phase is a continuous change in the order parameter and the second transition causes a discontinuous jump in the order parameter.
On the dynamics of mean-field equations for stochastic neural fields with delays
Touboul, Jonathan
2011-01-01
The cortex is composed of large-scale cell assemblies sharing the same individual properties and receiving the same input, in charge of certain functions, and subject to noise. Such assemblies are characterized by specific space locations and space-dependent delayed interactions. The mean-field equations for such systems were rigorously derived in a recent paper for general models, under mild assumptions on the network, using probabilistic methods. We summarize and investigate general implications of this result. We then address the dynamics of these stochastic neural field equations in the case of firing-rate neurons. This is a unique case where the very complex stochastic mean-field equations exactly reduce to a set of delayed differential or integro-differential equations on the two first moments of the solutions, this reduction being possible due to the Gaussian nature of the solutions. The obtained equations differ from more customary approaches in that it incorporates intrinsic noise levels nonlinearly ...
Analytical slave-spin mean-field approach to orbital selective Mott insulators
Komijani, Yashar; Kotliar, Gabriel
2017-09-01
We use the slave-spin mean-field approach to study particle-hole symmetric one- and two-band Hubbard models in the presence of Hund's coupling interaction. By analytical analysis of the Hamiltonian, we show that the locking of the two orbitals vs orbital selective Mott transition can be formulated within a Landau-Ginzburg framework. By applying the slave-spin mean field to impurity problems, we are able to make a correspondence between impurity and lattice. We also consider the stability of the orbital selective Mott phase to the hybridization between the orbitals and study the limitations of the slave-spin method for treating interorbital tunnelings in the case of multiorbital Bethe lattices with particle-hole symmetry.
Heterogeneous mean field for neural networks with short-term plasticity
di Volo, Matteo; Burioni, Raffaella; Casartelli, Mario; Livi, Roberto; Vezzani, Alessandro
2014-08-01
We report about the main dynamical features of a model of leaky integrate-and-fire excitatory neurons with short-term plasticity defined on random massive networks. We investigate the dynamics by use of a heterogeneous mean-field formulation of the model that is able to reproduce dynamical phases characterized by the presence of quasisynchronous events. This formulation allows one to solve also the inverse problem of reconstructing the in-degree distribution for different network topologies from the knowledge of the global activity field. We study the robustness of this inversion procedure by providing numerical evidence that the in-degree distribution can be recovered also in the presence of noise and disorder in the external currents. Finally, we discuss the validity of the heterogeneous mean-field approach for sparse networks with a sufficiently large average in-degree.
Macroscopic and large scale phenomena coarse graining, mean field limits and ergodicity
Rademacher, Jens; Zagaris, Antonios
2016-01-01
This book is the offspring of a summer school school “Macroscopic and large scale phenomena: coarse graining, mean field limits and ergodicity”, which was held in 2012 at the University of Twente, the Netherlands. The focus lies on mathematically rigorous methods for multiscale problems of physical origins. Each of the four book chapters is based on a set of lectures delivered at the school, yet all authors have expanded and refined their contributions. Francois Golse delivers a chapter on the dynamics of large particle systems in the mean field limit and surveys the most significant tools and methods to establish such limits with mathematical rigor. Golse discusses in depth a variety of examples, including Vlasov--Poisson and Vlasov--Maxwell systems. Lucia Scardia focuses on the rigorous derivation of macroscopic models using $\\Gamma$-convergence, a more recent variational method, which has proved very powerful for problems in material science. Scardia illustrates this by various basic examples and a mor...