Tunneling and Non-Universality in Continuum Percolation Systems

The values obtained experimentally for the conductivity critical exponent in numerous percolation systems, in which the interparticle conduction is by tunnelling, were found to be in the range of $t_0$ and about $t_0+10$, where $t_0$ is the universal conductivity exponent. These latter values are however considerably smaller than those predicted by the available ``one dimensional"-like theory of tunneling-percolation. In this letter we show that this long-standing discrepancy can be resolved by considering the more realistic "three dimensional" model and the limited proximity to the percolation threshold in all the many available experimental studiesComment: 4 pages, 2 figure

Theory of continuum percolation I. General formalism

The theoretical basis of continuum percolation has changed greatly since its beginning as little more than an analogy with lattice systems. Nevertheless, there is yet no comprehensive theory of this field. A basis for such a theory is provided here with the introduction of the Potts fluid, a system of interacting $s$-state spins which are free to move in the continuum. In the $s \to 1$ limit, the Potts magnetization, susceptibility and correlation functions are directly related to the percolation probability, the mean cluster size and the pair-connectedness, respectively. Through the Hamiltonian formulation of the Potts fluid, the standard methods of statistical mechanics can therefore be used in the continuum percolation problem.Comment: 26 pages, Late

The influence of strength of hyperon-hyperon interactions on neutron star properties

An equation of state of neutron star matter with strange baryons has been obtained. The effects of the strength of hyperon-hyperon interactions on the equations of state constructed for the chosen parameter sets have been analyzed. Numerous neutron star models show that the appearance of hyperons is connected with the increasing density in neutron star interiors. The performed calculations have indicated that the change of the hyperon-hyperon coupling constants affects the chemical composition of a neutron star. The obtained numerical hyperon star models exclude large population of strange baryons in the star interior.Comment: 18 pages, 22 figures, accepted to be published in Journal of Physics G: Nuclear and Particle Physic

Exact solution of a one-dimensional continuum percolation model

I consider a one dimensional system of particles which interact through a hard core of diameter \si and can connect to each other if they are closer than a distance $d$. The mean cluster size increases as a function of the density $\rho$ until it diverges at some critical density, the percolation threshold. This system can be mapped onto an off-lattice generalization of the Potts model which I have called the Potts fluid, and in this way, the mean cluster size, pair connectedness and percolation probability can be calculated exactly. The mean cluster size is S = 2 \exp[ \rho (d -\si)/(1 - \rho \si)] - 1 and diverges only at the close packing density \rho_{cp} = 1 / \si . This is confirmed by the behavior of the percolation probability. These results should help in judging the effectiveness of approximations or simulation methods before they are applied to higher dimensions.Comment: 21 pages, Late

Theory of continuum percolation III. Low density expansion

We use a previously introduced mapping between the continuum percolation model and the Potts fluid (a system of interacting s-states spins which are free to move in the continuum) to derive the low density expansion of the pair connectedness and the mean cluster size. We prove that given an adequate identification of functions, the result is equivalent to the density expansion derived from a completely different point of view by Coniglio et al. [J. Phys A 10, 1123 (1977)] to describe physical clustering in a gas. We then apply our expansion to a system of hypercubes with a hard core interaction. The calculated critical density is within approximately 5% of the results of simulations, and is thus much more precise than previous theoretical results which were based on integral equations. We suggest that this is because integral equations smooth out overly the partition function (i.e., they describe predominantly its analytical part), while our method targets instead the part which describes the phase transition (i.e., the singular part).Comment: 42 pages, Revtex, includes 5 EncapsulatedPostscript figures, submitted to Phys Rev

Are Radio Pulsars Strange Stars ?

A remarkably precise observational relation for pulse core component widths of radio pulsars is used to derive stringent limits on pulsar radii, strongly indicating that pulsars are strange stars rather than neutron stars. This is achieved by inclusion of general relativistic effects due to the pulsar mass on the size of the emission region needed to explain the observed pulse widths, which constrain the pulsar masses to be less than 2.5 Solar masses and radii to be smaller than 10.5 km.Comment: v.2 : 12 pages including 3 figures and 2 tables, LaTex, uses epsfig. This version has one extra figure, few lines of new text and typos fixe

Solution of the tunneling-percolation problem in the nanocomposite regime

We noted that the tunneling-percolation framework is quite well understood at the extreme cases of percolation-like and hopping-like behaviors but that the intermediate regime has not been previously discussed, in spite of its relevance to the intensively studied electrical properties of nanocomposites. Following that we study here the conductivity of dispersions of particle fillers inside an insulating matrix by taking into account explicitly the filler particle shapes and the inter-particle electron tunneling process. We show that the main features of the filler dependencies of the nanocomposite conductivity can be reproduced without introducing any \textit{a priori} imposed cut-off in the inter-particle conductances, as usually done in the percolation-like interpretation of these systems. Furthermore, we demonstrate that our numerical results are fully reproduced by the critical path method, which is generalized here in order to include the particle filler shapes. By exploiting this method, we provide simple analytical formulas for the composite conductivity valid for many regimes of interest. The validity of our formulation is assessed by reinterpreting existing experimental results on nanotube, nanofiber, nanosheet and nanosphere composites and by extracting the characteristic tunneling decay length, which is found to be within the expected range of its values. These results are concluded then to be not only useful for the understanding of the intermediate regime but also for tailoring the electrical properties of nanocomposites.Comment: 13 pages with 8 figures + 10 pages with 9 figures of supplementary material (Appendix B

Segregated tunneling-percolation model for transport nonuniversality

We propose a theory of the origin of transport nonuniversality in disordered insulating-conducting compounds based on the interplay between microstructure and tunneling processes between metallic grains dispersed in the insulating host. We show that if the metallic phase is arranged in quasi-one dimensional chains of conducting grains, then the distribution function of the chain conductivities g has a power-law divergence for g -> 0 leading to nonuniversal values of the transport critical exponent t. We evaluate the critical exponent t by Monte Carlo calculations on a cubic lattice and show that our model can describe universal as well nonuniversal behavior of transport depending on the value of few microstructural parameters. Such segregated tunneling-percolation model can describe the microstructure of a quite vast class of materials known as thick-film resistors which display universal or nonuniversal values of t depending on the composition.Comment: 8 pages, 5 figures (Phys. Rev. B - 1 August 2003)(fig1 replaced

Hyperon-hyperon interactions and properties of neutron matter

We present results from Brueckner-Hartree-Fock calculatons for beta stable neutron star matter with nucleonic and hyperonic degress degrees of freedom, employing the most recent parametrizations of the baryon-baryon interaction of the Nijmegen group. It is found that the only strange baryons emergin in beta stable matter up to total barionic densities of 1.2 fm^-3 are $\Sigma^-$ and $\Lambda$. The corresponding equations of state are then used to compute properties of neutron stars such as masses and radii.Comment: 27 pages, LateX, includes 8 PostScript figures, (submitted to PRC

The fading of SN 1997D

We present a new set of spectroscopic and photometric data extending the observations of SN 1997D to over 400 days after the explosion. These observations confirm the peculiar properties of SN 1997D, such as the very low abundance of 56Co (0.002 Msolar) and the low expansion velocity of the ejecta (~1000 km/s). We discuss the implications of these observations for the character of the progenitor and the nature of the remnant showing that a Crab-like pulsar or an accreting neutron star formed in the explosion of a low mass progenitor should already have produced a detectable luminosity at this epoch, in contrast with photometric data. On the other hand, the explosion of a high mass progenitor with the formation of a black hole is consistent with the available observations. The consequences of this conclusion regarding the nature of the explosion and the prospects of directly identifying the black hole are also addressed.Comment: 9 pages, 5 figures. Accepted for publication in MNRAS. Few typos have been correcte