Lyapunov exponents from geodesic spread in configuration space

The exact form of the Jacobi -- Levi-Civita (JLC) equation for geodesic spread is here explicitly worked out at arbitrary dimension for the configuration space manifold M_E = {q in R^N | V(q) < E} of a standard Hamiltonian system, equipped with the Jacobi (or kinetic energy) metric g_J. As the Hamiltonian flow corresponds to a geodesic flow on (M_E,g_J), the JLC equation can be used to study the degree of instability of the Hamiltonian flow. It is found that the solutions of the JLC equation are closely resembling the solutions of the standard tangent dynamics equation which is used to compute Lyapunov exponents. Therefore the instability exponents obtained through the JLC equation are in perfect quantitative agreement with usual Lyapunov exponents. This work completes a previous investigation that was limited only to two-degrees of freedom systems.Comment: REVTEX file, 10 pages, 2 figure

DLAs and Galaxy Formation

Damped Lyman-alpha systems (DLAs) are useful probes of star formation and galaxy formation at high redshift. We study the physical properties of DLAs and their relationship to Lyman-break galaxies using cosmological hydrodynamic simulations based on the concordance Lambda cold dark matter model. Fundamental statistics such as global neutral hydrogen (HI) mass density, HI column density distribution function, DLA rate-of-incidence and mean halo mass of DLAs are reproduced reasonably well by the simulations, but with some deviations that need to be understood better in the future. We discuss the feedback effects by supernovae and galactic winds on the DLA distribution. We also compute the [C_II] emission from neutral gas in high-z galaxies, and make predictions for the future observations by ALMA and SPICA. Agreement and disagreement between simulations and observations are discussed, as well as the future directions of our DLA research.Comment: 15 pages, 10 figures. Invited brief review for Modern Physics Letters A, in pres

Catching homologies by geometric entropy

A geometric entropy is defined as the Riemannian volume of the parameter space of a statistical manifold associated with a given network. As such it can be a good candidate for measuring networks complexity. Here we investigate its ability to single out topological features of networks proceeding in a bottom-up manner: first we consider small size networks by analytical methods and then large size networks by numerical techniques. Two different classes of networks, the random graphs and the scale--free networks, are investigated computing their Betti numbers and then showing the capability of geometric entropy of detecting homologies.Comment: 12 pages, 2 Figure

Galaxy Clustering at z~3

Galaxies at very high redshift (z~3 or greater) are now accessible to wholesale observation, making possible for the first time a robust statistical assessment of their spatial distribution at lookback times approaching ~90% of the age of the Universe. This paper summarizes recent progress in understanding the nature of these early galaxies, concentrating in particular on the clustering properties of photometrically selected ``Lyman break'' galaxies. Direct comparison of the data to predictions and physical insights provided by galaxy and structure formation models is particularly straightforward at these early epochs, and results in critical tests of the ``biased'', hierarchical galaxy formation paradigm.Comment: Presented at Royal Society Discussion Meeting, March 1998, "Large Scale Structure in the Universe", 14 pages LaTeX, 7 ps figures, uses rspublic.sty (included

Physical properties of 6dF dwarf galaxies

Spectral synthesis is basically the decomposition of an observed spectrum in terms of the superposition of a base of simple stellar populations of various ages and metallicities, producing as output the star formation and chemical histories of a galaxy, its extinction and velocity dispersion. The STARLIGHT code provides one of the most powerful spectral synthesis tools presently available. We have applied this code to the entire Six-Degree-Field Survey (6dF) sample of nearby star-forming galaxies, selecting dwarf galaxy candidates with the goal of: (1) deriving the age and metallicity of their stellar populations and (2) creating a database with the physical properties of our sample galaxies together with the FITS files of pure emission line spectra (i.e. the observed spectra after subtraction of the best-fitting synthetic stellar spectrum). Our results yield a good qualitative and quantitative agreement with previous studies based on the Sloan Digital Sky Survey (SDSS). However, an advantage of 6dF spectra is that they are taken within a twice as large fiber aperture, much reducing aperture effects in studies of nearby dwarf galaxies.Comment: To appear in JENAM Symposium "Dwarf Galaxies: Keys to Galaxy Formation and Evolution", P. Papaderos, S. Recchi, G. Hensler (eds.). Lisbon, September 2010, Springer Verlag, in pres

Thermodynamics of the Massive Gross-Neveu Model

We study the thermodynamics of massive Gross-Neveu models with explicitly broken discrete or continuous chiral symmetries for finite temperature and fermion densities. The large $N$ limit is discussed bearing attention to the no-go theorems for symmetry breaking in two dimensions which apply to the massless cases. The main purpose of the study is to serve as analytical orientation for the more complex problem of chiral transition in $4-$dimensional QCD with quarks. For any non-vanishing fermion mass we find, at finite densities, lines of first order phase transitions. For small mass values traces of would-be second order transitions and a tricritical point are recognizable. We study the thermodynamics of these models, and in the model with broken continuous chiral symmetry we examine the properties of the pion like state.Comment: 34 pages (+18 figures, available upon request to [email protected]), LATEX file, uses art12a.sty, macro included, UGVA-DPT 1994/06-85

Cosmological Conductive/Cooling Fronts as Lyman Alpha Forest Clouds

We propose a simple model for the origin and evolution of \lya clouds based on cosmological conductive/cooling fronts. In this model the \lya arises in the interfaces between the IGM and cold clouds that could be tentatively identified with protogalaxies. Most of the properties of the \lya absorbers are reproduced with a very restricted number of assumptions. Among these are the correct range of HI column density, cloud sizes and redshift and HI column density distributions for the absorbers. Several predictions and implications of the model are briefly discussed.Comment: 9 pages, plain TeX, 3 figures; ApJ Letters, accepte