Relativistic Equation of State for Core-Collapse Supernova Simulations

We construct the equation of state (EOS) of dense matter covering a wide range of temperature, proton fraction, and density for the use of core-collapse supernova simulations. The study is based on the relativistic mean-field (RMF) theory, which can provide an excellent description of nuclear matter and finite nuclei. The Thomas--Fermi approximation in combination with assumed nucleon distribution functions and a free energy minimization is adopted to describe the non-uniform matter, which is composed of a lattice of heavy nuclei. We treat the uniform matter and non-uniform matter consistently using the same RMF theory. We present two sets of EOS tables, namely EOS2 and EOS3. EOS2 is an update of our earlier work published in 1998 (EOS1), where only the nucleon degree of freedom is taken into account. EOS3 includes additional contributions from $\Lambda$ hyperons. The effect of $\Lambda$ hyperons on the EOS is negligible in the low-temperature and low-density region, whereas it tends to soften the EOS at high density. In comparison with EOS1, EOS2 and EOS3 have an improved design of ranges and grids, which covers the temperature range $T=0.1$--$10^{2.6}$ MeV with the logarithmic grid spacing $\Delta \log_{10}(T/\rm{[MeV]})=0.04$ (92 points including T=0), the proton fraction range $Y_p=0$--0.65 with the linear grid spacing $\Delta Y_p = 0.01$ (66 points), and the density range $\rho_B=10^{5.1}$--$10^{16}\,\rm{g\,cm^{-3}}$ with the logarithmic grid spacing $\Delta \log_{10}(\rho_B/\rm{[g\,cm^{-3}]}) = 0.1$ (110 points).Comment: 43 pages, 10 figure

Relativistic Equation of State of Nuclear Matter for Supernova Explosion

We construct the equation of state (EOS) of nuclear matter at finite temperature and density with various proton fractions within the relativistic mean field (RMF) theory for the use in the supernova simulations. The Thomas-Fermi approximation is adopted to describe the non-uniform matter where we consider nucleus, alpha-particle, proton and neutron in equilibrium. We treat the uniform matter and non-uniform matter consistently using the RMF theory. We tabulate the outcome as the pressure, free energy, entropy etc, with enough mesh points in wide ranges of the temperature, proton fraction, and baryon mass density.Comment: 22 pages, LaTeX, 9 ps-figures, Submitted to Prog.Theor.Phy

Sound absorption by clamped poroelastic plates

Measurements and predictions have been made of the absorption coefficient and the surface acoustic impedance of poroelastic plates clamped in a large impedance tube and separated from the rigid termination by an air gap. The measured and predicted absorption coefficient and surface impedance spectra exhibit low frequency peaks. The peak frequencies observed in the absorption coefficient are close to those predicted and measured in the deflection spectra of the clamped poroelastic plates. The influences of the rigidity of the clamping conditions and the width of the air gap have been investigated. Both influences are found to be important. Increasing the rigidity of clamping reduces the low frequency absorption peaks compared with those measured for simply supported plates or plates in an intermediate clamping condition. Results for a closed cell foam plate and for two open cell foam plates made from recycled materials are presented. For identical clamping conditions and width of air gap, the results for the different materials differ as a consequence mainly of their different elasticity, thickness, and cell structure

Scaling regimes and critical dimensions in the Kardar-Parisi-Zhang problem

We study the scaling regimes for the Kardar-Parisi-Zhang equation with noise correlator R(q) ~ (1 + w q^{-2 \rho}) in Fourier space, as a function of \rho and the spatial dimension d. By means of a stochastic Cole-Hopf transformation, the critical and correction-to-scaling exponents at the roughening transition are determined to all orders in a (d - d_c) expansion. We also argue that there is a intriguing possibility that the rough phases above and below the lower critical dimension d_c = 2 (1 + \rho) are genuinely different which could lead to a re-interpretation of results in the literature.Comment: Latex, 7 pages, eps files for two figures as well as Europhys. Lett. style files included; slightly expanded reincarnatio

Frustrated Spin System in theta-(BEDT-TTF)_2RbZn(SCN)_4

The origin of the spin gap behavior in the low-temperature dimerized phase of theta-(BEDT-TTF)_2RbZn(SCN)_4 has been theoretically studied based on the Hartree-Fock approximation for the on-site Coulomb interaction at absolute zero. Calculations show that, in the parameter region considered to be relevant to this compound, antiferromagnetic ordering is stabilized between dimers consisting of pairs of molecules coupled with the largest transfer integral. Based on this result an effective localized spin 1/2 model is constructed which indicates the existence of the frustration among spins. This frustration may result in the formation of spin gap.Comment: 4 pages, 5 figures, to be published in J. Phys. Soc. Jpn. 67 (1998) no.

Minority Game With Peer Pressure

To study the interplay between global market choice and local peer pressure, we construct a minority-game-like econophysical model. In this so-called networked minority game model, every selfish player uses both the historical minority choice of the population and the historical choice of one's neighbors in an unbiased manner to make decision. Results of numerical simulation show that the level of cooperation in the networked minority game differs remarkably from the original minority game as well as the prediction of the crowd-anticrowd theory. We argue that the deviation from the crowd-anticrowd theory is due to the negligence of the effect of a four point correlation function in the effective Hamiltonian of the system.Comment: 10 pages, 3 figures in revtex 4.

Electrovacuum Near-horizon Geometries in Four and Five Dimensions

Associated to every stationary extremal black hole is a unique near-horizon geometry, itself a solution of the field equations. These latter spacetimes are more tractable to analyze and most importantly, retain properties of the original black hole which are intrinsic to the event horizon. After reviewing general features of near-horizon geometries, such as SO(2,1) symmetry enhancement, I report on recent work on stationary, charged extremal black hole solutions of the Einstein-Maxwell equations with a negative cosmological constant in four dimensions and present a classification of near-horizon geometries of black holes on this kind. In five dimensions, charged extremal black hole solutions to minimal (gauged) supergravity, which arises naturally in string theory and the gauge theory/gravity correspondence, are considered. I consider the classification of near-horizon geometries for the subset of such black holes which are supersymmetric. Recent progress on the classification problem in the general extremal, non-supersymmetric case is also discussed.Comment: Invited contribution to a special issue of Classical and Quantum Gravity on the 19th International Conference on General Relativity and Gravitation, Mexico City, July 5-9, 201