Order in Binary Sequences and the Routes to Chaos

The natural order in the space of binary sequences permits to recover the $U$-sequence. Also the scaling laws of the period-doubling cascade and the intermittency route to chaos defined in that ordered set are explained. These arise as intrinsic properties of this ordered set, and independent from any consideration about dynamical systems.Comment: 13 pages, 2 table

A Reverse Monte Carlo study of H+D Lyman alpha absorption from QSO spectra

A new method based on a Reverse Monte Carlo [RMC] technique and aimed at the inverse problem in the analysis of interstellar (intergalactic) absorption lines is presented. The line formation process in chaotic media with a finite correlation length $(l > 0)$ of the stochastic velocity field (mesoturbulence) is considered. This generalizes the standard assumption of completely uncorrelated bulk motions $(l \equiv 0)$ in the microturbulent approximation which is used for the data analysis up-to-now. It is shown that the RMC method allows to estimate from an observed spectrum the proper physical parameters of the absorbing gas and simultaneously an appropriate structure of the velocity field parallel to the line-of-sight. The application to the analysis of the H+D Ly$\alpha$ profile is demonstrated using Burles & Tytler [B&T] data for QSO 1009+2956 where the DI Ly$\alpha$ line is seen at $z_a = 2.504$. The results obtained favor a low D/H ratio in this absorption system, although our upper limit for the hydrogen isotopic ratio of about $4.5\times10^{-5}$ is slightly higher than that of B&T (D/H = $3.0^{+0.6}_{-0.5} \times 10^{-5}$). We also show that the D/H and N(HI) values are, in general, correlated, i.e. the derived D-abundance may be badly dependent on the assumed hydrogen column density. The corresponding confidence regions for an arbitrary and a fixed stochastic velocity field distribution are calculated.Comment: 6 pages, LaTeX, 2 Postscript figures, to appear in "The Primordial Nuclei and Their Galactic Evolution", eds. N. Prantzos, M. Tosi, R. von Steiger (Kluwer: Dordrecht

Koszul Theorem for S-Lie coalgebras

For a symmetry braid S-Lie coalgebras, as a dual object to algebras introduced by Gurevich, are considered. For an Young antisymmetrizer an S-exterior algebra is introduced. From this differential point of view S-Lie coalgebras are investigated. The dual Koszul theorem in this case is proved.Comment: 8 pages, AMSLaTe

Aging in the Linear Harmonic Oscillator

The low temperature Monte Carlo dynamics of an ensemble of linear harmonic oscillators shows some entropic barriers related to the difficulty of finding the directions in configurational space which decrease the energy. This mechanism is enough to observe some typical non-equilibrium features of glassy systems like activated-type behavior and aging in the correlation function and in the response function. Due to the absence of interactions the model only displays a one-step relaxation process.Comment: 6 pages revtex including 3 figures in postscrip

A Generalization of Metropolis and Heat-Bath Sampling for Monte Carlo Simulations

For a wide class of applications of the Monte Carlo method, we describe a general sampling methodology that is guaranteed to converge to a specified equilibrium distribution function. The method is distinct from that of Metropolis in that it is sometimes possible to arrange for unconditional acceptance of trial moves. It involves sampling states in a local region of phase space with probability equal to, in the first approximation, the square root of the desired global probability density function. The validity of this choice is derived from the Chapman-Kolmogorov equation, and the utility of the method is illustrated by a prototypical numerical experiment.Comment: RevTeX, 7 pages, 2 table

Phase diagram of four-dimensional dynamical triangulations with a boundary

We report on simulations of DT simplicial gravity for manifolds with the topology of the 4-disk. We find evidence for four phases in a two-dimensional parameter space. In two of these the boundary plays no dynamical role and the geometries are equivalent to those observed earlier for the sphere $S^4$. In another phase the boundary is maximal and the quantum geometry degenerates to a one dimensional branched polymer. In contrast we provide evidence that the fourth phase is effectively three-dimensional. We find discontinuous phase transitions at all the phase boundaries.Comment: 13 pages, late

Power sums of Coxeter exponents

Consider an irreducible finite Coxeter system. We show that for any nonnegative integer n the sum of the nth powers of the Coxeter exponents can be written uniformly as a polynomial in four parameters: h (the Coxeter number), r (the rank), and two further parameters.Comment: 14 page

Estimation of microscopic averages from metadynamics

With the help of metadynamics it is possible to calculate efficiently the free energy of systems displaying high energy barriers as a function of few selected "collective variables". In doing this, the contribution of all the other degrees of freedom ("microscopic" variables) is averaged out and, thus, lost. In the following, it is shown that it is possible to calculate the thermal average of these microscopic degrees of freedom during the metadynamics, not loosing this piece of information

BAT - The Bayesian Analysis Toolkit

We describe the development of a new toolkit for data analysis. The analysis package is based on Bayes' Theorem, and is realized with the use of Markov Chain Monte Carlo. This gives access to the full posterior probability distribution. Parameter estimation, limit setting and uncertainty propagation are implemented in a straightforward manner. A goodness-of-fit criterion is presented which is intuitive and of great practical use.Comment: 31 pages, 10 figure

Morphological instabilities of a thin film on a Penrose lattice: a Monte Carlo study

We computed by a Monte Carlo method the thermal relaxation of a polycrystalline thin film deposited on a Penrose lattice. The thin film was modelled by a 2 dimensional array of elementary domains, which have each a given height. During the Monte Carlo process, the height of each of these elementary domains is allowed to change as well as their crystallographic orientation. After equilibrium is reached at a given numerical temperature, all elementary domains have changed their orientation into the same one and small islands appear, preferentially on the domains of the Penrose lattice located in the center of heptagons. This method is a new numerical approach to study the influence of the substrate and its defects on the islanding process of polycrystalline films.Comment: 9 pages,5 figure