Bright and dark breathers in Fermi-Pasta-Ulam lattices

In this paper we study the existence and linear stability of bright and dark breathers in one-dimensional FPU lattices. On the one hand, we test the range of validity of a recent breathers existence proof [G. James, {\em C. R. Acad. Sci. Paris}, 332, Ser. 1, pp. 581 (2001)] using numerical computations. Approximate analytical expressions for small amplitude bright and dark breathers are found to fit very well exact numerical solutions even far from the top of the phonon band. On the other hand, we study numerically large amplitude breathers non predicted in the above cited reference. In particular, for a class of asymmetric FPU potentials we find an energy threshold for the existence of exact discrete breathers, which is a relatively unexplored phenomenon in one-dimensional lattices. Bright and dark breathers superposed on a uniformly stressed static configuration are also investigated.Comment: 11 pages, 16 figure

Breathers in FPU systems, near and far from the phonon band

There exists a recent mathematical proof on the existence of small amplitude breathers in FPU systems near the phonon band, which includes a prediction of their amplitude and width. In this work we obtain numerically these breathers, and calculate the range of validity of the predictions, which extends relatively far from the phonon band. There exist also large amplitude breathers with the same frequency, with the consequence that there is an energy gap for breather creation in these systems.Comment: 3 pages, 2 figures, proceeding of the conference on Localization and to and Energy Transfer in Nonlinear Systems, June 17-21, 2002, San Lorenzo de El Escorial, Madrid, Spain. To be published by World Scientifi

A fluidized granular medium as an instance of the Fluctuation Theorem

We study the statistics of the power flux into a collection of inelastic beads maintained in a fluidized steady-state by external mechanical driving. The power shows large fluctuations, including frequent large negative fluctuations, about its average value. The relative probabilities of positive and negative fluctuations in the power flux are in close accord with the Fluctuation Theorem of Gallavotti and Cohen, even at time scales shorter than those required by the theorem. We also compare an effective temperature that emerges from this analysis to the kinetic granular temperature.Comment: 4 pages, 5 figures, submited to Physical Review Letters; Revised versio

Statistical isotropy of the Cosmic Microwave Background

The breakdown of statistical homogeneity and isotropy of cosmic perturbations is a generic feature of ultra large scale structure of the cosmos, in particular, of non trivial cosmic topology. The statistical isotropy (SI) of the Cosmic Microwave Background temperature fluctuations (CMB anisotropy) is sensitive to this breakdown on the largest scales comparable to, and even beyond the cosmic horizon. We propose a set of measures, $\kappa_\ell$ ($\ell=1,2,3, ...$) which for non-zero values indicate and quantify statistical isotropy violations in a CMB map. We numerically compute the predicted $\kappa_\ell$ spectra for CMB anisotropy in flat torus universe models. Characteristic signature of different models in the $\kappa_\ell$ spectrum are noted.Comment: Presented at PASCOS'03, January 3-8, 2003, in TIFR, Mumbai; to be published in a special issue of 'Pramana' (4 pages, 1 figure, style files included

Topology of the Universe: background and recent observational approaches

Is the Universe (a spatial section thereof) finite or infinite? Knowing the global geometry of a Friedmann-Lema\^{\i}tre (FL) universe requires knowing both its curvature and its topology. A flat or hyperbolic (``open'') FL universe is {\em not} necessarily infinite in volume. Multiply connected flat and hyperbolic models are, in general, as consistent with present observations on scales of 1-20{\hGpc} as are the corresponding simply connected flat and hyperbolic models. The methods of detecting multiply connected models (MCM's) are presently in their pioneering phase of development and the optimal observationally realistic strategy is probably yet to be calculated. Constraints against MCM's on ~1-4 h^{-1} Gpc scales have been claimed, but relate more to inconsistent assumptions on perturbation statistics rather than just to topology. Candidate 3-manifolds based on hypothesised multiply imaged objects are being offered for observational refutation. The theoretical and observational sides of this rapidly developing subject have yet to make any serious contact, but the prospects of a significant detection in the coming decade may well propel the two together.Comment: 5 pages, proceedings of the Workshop ``Cosmology: Observations Confront Theories,'' 11-17 Jan 1999, IIT Kharagpur, West Bengal, to appear in Pramana - Journal of Physic

A measure on the set of compact Friedmann-Lemaitre-Robertson-Walker models

Compact, flat Friedmann-Lemaitre-Robertson-Walker (FLRW) models have recently regained interest as a good fit to the observed cosmic microwave background temperature fluctuations. However, it is generally thought that a globally, exactly-flat FLRW model is theoretically improbable. Here, in order to obtain a probability space on the set F of compact, comoving, 3-spatial sections of FLRW models, a physically motivated hypothesis is proposed, using the density parameter Omega as a derived rather than fundamental parameter. We assume that the processes that select the 3-manifold also select a global mass-energy and a Hubble parameter. The inferred range in Omega consists of a single real value for any 3-manifold. Thus, the obvious measure over F is the discrete measure. Hence, if the global mass-energy and Hubble parameter are a function of 3-manifold choice among compact FLRW models, then probability spaces parametrised by Omega do not, in general, give a zero probability of a flat model. Alternatively, parametrisation by the injectivity radius r_inj ("size") suggests the Lebesgue measure. In this case, the probability space over the injectivity radius implies that flat models occur almost surely (a.s.), in the sense of probability theory, and non-flat models a.s. do not occur.Comment: 19 pages, 4 figures; v2: minor language improvements; v3: generalisation: m, H functions of

Reversible Diffusion-Limited Reactions: "Chemical Equilibrium" State and the Law of Mass Action Revisited

The validity of two fundamental concepts of classical chemical kinetics - the notion of "Chemical Equilibrium" and the "Law of Mass Action" - are re-examined for reversible \textit{diffusion-limited} reactions (DLR), as exemplified here by association/dissociation $A+A \rightleftharpoons B$ reactions. We consider a general model of long-ranged reactions, such that any pair of $A$ particles, separated by distance $\mu$, may react with probability $\omega_+(\mu)$, and any $B$ may dissociate with probability $\omega_-(\lambda)$ into a geminate pair of $A$s separated by distance $\lambda$. Within an exact analytical approach, we show that the asymptotic state attained by reversible DLR at $t = \infty$ is generally \textit{not a true thermodynamic equilibrium}, but rather a non-equilibrium steady-state, and that the Law of Mass Action is invalid. The classical picture holds \text{only} in physically unrealistic case when $\omega_+(\mu) \equiv \omega_-(\mu)$ for any value of $\mu$.Comment: 4 page

Recursos minerales marinos en las rías gallegas y en la plataforma continental adyacente.

La riqueza natural de las rías gallegas y de su plataforma adyacente no se restringe exclusivamente a las pesquerías. Los recursos minerales marinos, entre los que se encuentran los áridos, placeres, sal marina, fosforitas, hidrocarburos e hidratos de gas poseen un interés económico intrínseco muy importante. Aunque las explotaciones de sal marina tuvieron importancia histórica en Galicia, en la actualidad el aprovechamiento económico de los recursos minerales marinos se limita a los áridos empleados en la regeneración de playas. Una compleja interacción de factores jurídicos, tecnológicos y económicos ha inhibido hasta ahora el desarrollo de otros recursos. Sin embargo, el nuevo orden político y económico internacional proporciona un escenario muy distinto que facilita su explotación. Sensibles a este cambio, las instituciones responsables han impulsado el desarrollo de programas de evaluación de algunos de estos recursos, cuyos resultados se exponen aquí. Este es el caso de los hidrocarburos, de interés energético estratégico, o de los placeres cuyo interés se basa en la presencia de ciertos metales y tierras raras empleados en los nuevos materiales. En este sentido es deseable que en los próximos años se considere también la evaluación de recursos energéticos alternativos como los hidratos de gas, o de otros que como las fosforitas, poseen un interés estratégico especial para la creciente demanda de fertilizantes que anticipa la racionalización del sector agropecuario en la región. Sólo una completa evaluación del potencial económico de 67 G. Méndez et al. Recursos minerales marinos en las rías gallegas... todos los recursos minerales marinos en Galicia permitirá planificar una política de desarrollo sostenido adecuada.The natural wealth of the Galician rias and adjoining platform is not constrained to their well know fisheries. Their marine mineral resources, such as aggregates, placers, marine salt, phosphorites, hydrocarbons and gas hydrates, also have very significant intrinsic economic value. Despite a number of marine salt exploitations of historical relevance, the economic importance of marine mineral mining in Galicia, at present day, is limited to aggregates for beach renourishment. A complex interaction of legal, technological and economical factors has inhibited the development of other resources. However, the new international political and economical order has provided a very different scenario that favours their exploitation. Sensitive to this change, the relevant institutions have put in place evaluation programs for some of these resources, whose results will be shown here. This is the case of hydrocarbons, of strategic energy interest, or placers a source of metals and rare-earth elements for the new materials industry. In this sense it is desirable that alternative energy resources like gas hydrates, or strategically interesting resources for agriculture like phosphorites will be adequately evaluated in the next few years. Only a complete evaluation of the true economical importance of all the marine mineral resources in Galicia will allow adequate long-term planning of successful sustained development policies

Functional Approach to Stochastic Inflation

We propose functional approach to the stochastic inflationary universe dynamics. It is based on path integral representation of the solution to the differential equation for the scalar field probability distribution. In the saddle-point approximation scalar field probability distributions of various type are derived and the statistics of the inflationary-history-dependent functionals is developed.Comment: 20 pages, Preprint BROWN-HET-960, uses phyzz