Calculation of percolation thresholds in high dimensions for fcc, bcc, and diamond lattices

In a recent article, Galam and Mauger proposed an invariant for site and bond percolation thresholds, based on known values for twenty lattices (Eur. Phys. J. B 1 (1998) 255-258). Here we give a larger list of values for more than forty lattices in two to six dimensions. In this list are new results for fcc, bcc, and diamond lattices in 4, 5, and 6 dimensions. The list contains examples of lattices with equal site percolation thresholds, but different bond percolation thresholds. These and other examples show that there are deviations from the proposed invariant of up to 12% in two dimensions, increasing to 69% in higher dimensions.Comment: 12 pages, 3 figures (EPS), LaTe

What is the optimal shape of a fin for one dimensional heat conduction?

This article is concerned with the shape of small devices used to control the heat flowing between a solid and a fluid phase, usually called \textsl{fin}. The temperature along a fin in stationary regime is modeled by a one-dimensional Sturm-Liouville equation whose coefficients strongly depend on its geometrical features. We are interested in the following issue: is there any optimal shape maximizing the heat flux at the inlet of the fin? Two relevant constraints are examined, by imposing either its volume or its surface, and analytical nonexistence results are proved for both problems. Furthermore, using specific perturbations, we explicitly compute the optimal values and construct maximizing sequences. We show in particular that the optimal heat flux at the inlet is infinite in the first case and finite in the second one. Finally, we provide several extensions of these results for more general models of heat conduction, as well as several numerical illustrations

Spectral methods in general relativistic astrophysics

We present spectral methods developed in our group to solve three-dimensional partial differential equations. The emphasis is put on equations arising from astrophysical problems in the framework of general relativity.Comment: 51 pages, elsart (Elsevier Preprint), 19 PostScript figures, submitted to Journal of Computational & Applied Mathematic

A phase transition due to thick vortices in SU(2) lattice gauge theory

SU(2) lattice gauge theory is studied after eliminating thin monopoles and the smallest thick monopoles. Kinematically this constraint allows thick vortex loops which produce long range Z(2) fluctuations. The thick vortex loops are identified in a three dimensional simulation. A condensate of thick vortices persists even after the thin vortices have all disappeared. They decouple at a slightly lower temperature (higher $\beta$) than the thin vortices and drive a Z(2) like phase transition.Comment: 3 pages, 3 figures (ps), Lattice 2002(Topology

Gravitational signals due to tidal interactions between white dwarfs and black holes

In this paper we compute the gravitational signal emitted when a white dwarf moves around a black hole on a closed or open orbit using the affine model approach. We compare the orbital and the tidal contributions to the signal, assuming that the star moves in a safe region where, although very close to the black hole, the strength of the tidal interaction is insufficient to provoque the stellar disruption. We show that for all considered orbits the tidal signal presents sharp peaks corresponding to the excitation of the star non radial oscillation modes, the amplitude of which depends on how deep the star penetrates the black hole tidal radius and on the type of orbit. Further structure is added to the emitted signal by the coupling between the orbital and the tidal motion.Comment: 21 pages, 8 figres. Submitted to MNRA

An investigation of site-bond percolation on many lattices

A calculation of site-bond percolation thresholds in many lattices in two to five dimensions is presented. The line of threshold values has been parametrized in the literature, but we show here that there are strong deviations from the known approximate equations. We propose an alternative parametrization that lies much closer to the numerical valuesComment: LaTeX, 14 pages, 6 figures, 5 tables, submitted to Int. J. Mod. Phys.

Merger of black hole-neutron star binaries: nonspinning black hole case

We perform a simulation for merger of a black hole (BH)-neutron star (NS) binary in full general relativity preparing a quasicircular state as initial condition. The BH is modeled by a moving puncture with no spin and the NS by the $\Gamma$-law equation of state with $\Gamma=2$. Corotating velocity field is assumed for the NS. The mass of the BH and the rest-mass of the NS are chosen to be $\approx 3.2 M_{\odot}$ and $\approx 1.4 M_{\odot}$ with relatively large radius of the NS $\approx 14$ km. The NS is tidally disrupted near the innermost stable orbit but $\sim 80$ of the material is swallowed into the BH with small disk mass $\sim 0.3M_{\odot}$ even for such small BH mass $\sim 3M_{\odot}$. The result indicates that the system of a BH and a massive disk of $\sim M_{\odot}$ is not formed from nonspinning BH-NS binaries, although a disk of mass $\sim 0.1M_{\odot}$ is a possible outcome.Comment: 5 pages. Phys. Rev. D 74, 121503 (R) (2006