Manifolds on the verge of a hyperbolicity breakdown

We study numerically the disappearance of normally hyperbolic invariant tori in quasiperiodic systems and identify a scenario for their breakdown. In this scenario, the breakdown happens because two invariant directions of the transversal dynamics come close to each other, losing their regularity. On the other hand, the Lyapunov multipliers associated with the invariant directions remain more or less constant. We identify notable quantitative regularities in this scenario, namely that the minimum angle between the two invariant directions and the Lyapunov multipliers have power law dependence with the parameters. The exponents of the power laws seem to be universal.

Experiments on anisotropic radial viscous fingering

We observe dendritic patterns in fluid flow in an anisotropic Hele-Shaw cell and measure the tip shapes and trajectories of individual dendritic branches under conditions where the pattern growth appears to be dominated by surface tension anisotropy and also under conditions where kinetic effects appear dominant. In each case, the tip position depends on a power law in the time, but the exponent of this power law can vary significantly among flow realizations. Averaging many growth exponents a yields a =0.640.09 in the surface tension dominated regime and a =0.660.09 in the kinetic regime. Restricting the analysis to realizations when a is very close to 0.6 shows great regularity across pattern regimes in the coefficient of the temporal dependence of the tip trajectory.

Wave propagation in a medium with disordered excitability

The effect of quenched disorder on the propagation of autowaves in excitable media is studied both experimentally and numerically in relation to the light-sensitive Belousov-Zhabotinsky reaction. The spatial disorder is introduced through a random distribution with two different levels of transmittance. In one dimension the (time-averaged) wave speed is smaller than the corresponding to a homogeneous medium with the mean excitability. Contrarily, in two dimensions the velocity increases due to the roughening of the front. Results are interpreted using kinematic and scaling arguments. In particular, for d = 2 we verify a theoretical prediction of a power-law dependence for the relative change of the propagation speed on the disorder amplitude.

Brittle to ductile transition in a fiber bundle with strong heterogeneity

We analyze the failure process of a two-component system with widely different fracture strength in the framework of a fiber bundle model with localized load sharing. A fraction 0≤α≤1 of the bundle is strong and it is represented by unbreakable fibers, while fibers of the weak component have randomly distributed failure strength. Computer simulations revealed that there exists a critical composition αc which separates two qualitatively different behaviors: Below the critical point, the failure of the bundle is brittle, characterized by an abrupt damage growth within the breakable part of the system. Above αc, however, the macroscopic response becomes ductile, providing stability during the entire breaking process. The transition occurs at an astonishingly low fraction of strong fibers which can have importance for applications. We show that in the ductile phase, the size distribution of breaking bursts has a power law functional form with an exponent μ=2 followed by an exponential cutoff. In the brittle phase, the power law also prevails but with a higher exponent μ=92. The transition between the two phases shows analogies to continuous phase transitions. Analyzing the microstructure of the damage, it was found that at the beginning of the fracture process cracks nucleate randomly, while later on growth and coalescence of cracks dominate, which give rise to power law distributed crack sizes.

Holographic collisions in confining theories

We study the gravitational dual of a high-energy collision in a confining gauge theory. We consider a linearized approach in which two point particles traveling in an AdS-soliton background suddenly collide to form an object at rest (presumably a black hole for large enough center-of-mass energies). The resulting radiation exhibits the features expected in a theory with a mass gap: late-time power law tails of the form t −3/2, the failure of Huygens" principle and distortion of the wave pattern as it propagates. The energy spectrum is exponentially suppressed for frequencies smaller than the gauge theory mass gap. Consequently, we observe no memory effect in the gravitational waveforms. At larger frequencies the spectrum has an upward-stairway structure, which corresponds to the excitation of the tower of massive states in the confining gauge theory. We discuss the importance of phenomenological cutoffs to regularize the divergent spectrum, and the aspects of the full non-linear collision that are expected to be captured by our approach.

Identifying the preferred subset of enzymatic profiles in nonlinear kinetic metabolic models via multiobjective global optimization and pareto filters

Optimization models in metabolic engineering and systems biology focus typically on optimizing a unique criterion, usually the synthesis rate of a metabolite of interest or the rate of growth. Connectivity and non-linear regulatory effects, however, make it necessary to consider multiple objectives in order to identify useful strategies that balance out different metabolic issues. This is a fundamental aspect, as optimization of maximum yield in a given condition may involve unrealistic values in other key processes. Due to the difficulties associated with detailed non-linear models, analysis using stoichiometric descriptions and linear optimization methods have become rather popular in systems biology. However, despite being useful, these approaches fail in capturing the intrinsic nonlinear nature of the underlying metabolic systems and the regulatory signals involved. Targeting more complex biological systems requires the application of global optimization methods to non-linear representations. In this work we address the multi-objective global optimization of metabolic networks that are described by a special class of models based on the power-law formalism: the generalized mass action (GMA) representation. Our goal is to develop global optimization methods capable of efficiently dealing with several biological criteria simultaneously. In order to overcome the numerical difficulties of dealing with multiple criteria in the optimization, we propose a heuristic approach based on the epsilon constraint method that reduces the computational burden of generating a set of Pareto optimal alternatives, each achieving a unique combination of objectives values. To facilitate the post-optimal analysis of these solutions and narrow down their number prior to being tested in the laboratory, we explore the use of Pareto filters that identify the preferred subset of enzymatic profiles. We demonstrate the usefulness of our approach by means of a case study that optimizes the ethanol production in the fermentation of Saccharomyces cerevisiae.

Predicción de la resistencia al flujo en ríos de montaña

Se han calibrado, validado y comparado tres modelos de resistencia al flujo de contorno granular: un modelo potencial y otros dos modelos desarrollados para condiciones de alta rugosidad relativa (uno basado en una modificación de la ley logarítmica de Prandtl-von Karman y otro fundamentado en un perfil de velocidad configurado en dos zonas: una uniforme en las proximidades de los elementos de rugosidad y otra superior que sigue una distribución logarítmica). Se ha empleado para ello un numeroso conjunto de 1.533 datos tomados en ríos y en canales de laboratorio, representativo de un amplio intervalo hidráulico y geomorfológico en el ámbito de ríos de grava y de montaña. Han resultado preferibles las ecuaciones ajustadas con los percentiles granulométricos mayores (d90 o d84) que las ajustadas con el diámetro mediano (d50), debido a la mayor capacidad explicativa alcanzada dado un modelo, la menor diferencia en la bondad de ajuste entre los diferentes modelos y la menor influencia del origen de los datos (río o canal de laboratorio). Las ecuaciones ajustadas de acuerdo con los modelos en donde se contemplan condiciones de alta rugosidad relativa presentan predicciones similares, exceptuando el intervalo macrorrugoso (y/d90 < 1), en el que es preferible la correspondiente al modelo fundamentado en el perfil de velocidad configurado en dos zonas. Se recomienda restringir la aplicación de la ecuación ajustada con arreglo a la ley potencial al intervalo de y/d90 comprendido entre uno y veinte, puesto que fuera de dicho intervalo tiende a infraestimar notablemente la resistencia al flujo.

Percolation of spatially constrained Erdos-R enyi networks with degree correlations

Motivated by experiments on activity in neuronal cultures [J. Soriano, M. Rodr ́ıguez Mart́ınez, T. Tlusty, and E. Moses, Proc. Natl. Acad. Sci. 105, 13758 (2008)], we investigate the percolation transition and critical exponents of spatially embedded Erd̋os-Ŕenyi networks with degree correlations. In our model networks, nodes are randomly distributed in a two-dimensional spatial domain, and the connection probability depends on Euclidian link length by a power law as well as on the degrees of linked nodes. Generally, spatial constraints lead to higher percolation thresholds in the sense that more links are needed to achieve global connectivity. However, degree correlations favor or do not favor percolation depending on the connectivity rules. We employ two construction methods to introduce degree correlations. In the first one, nodes stay homogeneously distributed and are connected via a distance- and degree-dependent probability. We observe that assortativity in the resulting network leads to a decrease of the percolation threshold. In the second construction methods, nodes are first spatially segregated depending on their degree and afterwards connected with a distance-dependent probability. In this segregated model, we find a threshold increase that accompanies the rising assortativity. Additionally, when the network is constructed in a disassortative way, we observe that this property has little effect on the percolation transition.

A simple model to describe the thixotropic behavior of paints.

We propose a simple rheological model to describe the thixotropic behavior of paints, since the classical hysteresis area, which is usually used, is not enough to evaluate thixotropy. The model is based on the assumption that viscosity is a direct measure of the structural level of the paint. The model depends on two equations: the Cross-Carreau equation to describe the equilibrium viscosity and a second order kinetic equation to express the time dependence of viscosity. Two characteristic thixotropic times are differentiated: one for the net structure breakdown, which is defined as a power law function of shear rate, and an other for the net structure buildup, which is not dependent on the shear rate. The knowledge of both kinetic processes can be used to improve the quality and applicability of paints. Five representative commercial protective marine paints are tested. They are based on chlorinated rubber, acrylic, alkyd, vinyl, and epoxy resins. The temperature dependence of the rheological behavior is also studied with the temperature ranging from 5 ºC to 35 ºC. It is found that the paints exhibit both shear thinning and thixotropic behavior. The model fits satisfactorily the thixotropy of the studied paints. It is also able to predict the thixotropy dependence on temperature. Both viscosity and the degree of thixotropy increase as the temperature decreases.

Observation of VHE γ-rays from Cassiopeia A with the MAGIC telescope

Aims:We searched for very high energy (VHE) γ-ray emission from the supernova remnant Cassiopeia A Methods: The shell-type supernova remnant Cassiopeia A was observed with the 17 m MAGIC telescope between July 2006 and January 2007 for a total time of 47 h. Results: The source was detected above an energy of 250 GeV with a significance of 5.2σ and a photon flux above 1 TeV of (7.3 ± 0.7_stat ± 2.2_sys) × 10-13 cm-2s-1. The photon spectrum is compatible with a power law dN/dE ∝ E-Γ with a photon index Γ = 2.3 ± 0.2_stat ± 0.2_sys. The source is point-like within the angular resolution of the telescope.

Local thermodynamics and the generalized Gibbs-Duhem equation in systems with long-range interactions

The local thermodynamics of a system with long-range interactions in d dimensions is studied using the mean-field approximation. Long-range interactions are introduced through pair interaction potentials that decay as a power law in the interparticle distance. We compute the local entropy, Helmholtz free energy, and grand potential per particle in the microcanonical, canonical, and grand canonical ensembles, respectively. From the local entropy per particle we obtain the local equation of state of the system by using the condition of local thermodynamic equilibrium. This local equation of state has the form of the ideal gas equation of state, but with the density depending on the potential characterizing long-range interactions. By volume integration of the relation between the different thermodynamic potentials at the local level, we find the corresponding equation satisfied by the potentials at the global level. It is shown that the potential energy enters as a thermodynamic variable that modifies the global thermodynamic potentials. As a result, we find a generalized Gibbs-Duhem equation that relates the potential energy to the temperature, pressure, and chemical potential. For the marginal case where the power of the decaying interaction potential is equal to the dimension of the space, the usual Gibbs-Duhem equation is recovered. As examples of the application of this equation, we consider spatially uniform interaction potentials and the self-gravitating gas. We also point out a close relationship with the thermodynamics of small systems.

Long-term X-ray variability of the microquasar system LS5039/RX J1826.2-1450

We report on the results of the spectral and timing analysis of a BeppoSAX observation of the microquasar system LS 5039/RX J1826.2-1450. The source was found in a low-flux state with Fx(1-10 keV)= 4.7 x 10^{-12} erg cm^{-2} s^{-1}, which represents almost one order of magnitude lower than a previous RXTE observation 2.5 years before. The 0.1--10 keV spectrum is described by an absorbed power-law continuum with photon-number spectral index Gamma=1.8+-0.2 and hydrogen column density of NH=1.0^{+0.4}_{-0.3} x 10^{22} cm^{-2}. According to the orbital parameters of the system the BeppoSAX observation covers the time of an X-ray eclipse should one occur. However, the 1.6-10 keV light curve does not show evidence for such an event, which allows us to give an upper limit to the inclination of the system. The low X-ray flux detected during this observation is interpreted as a decrease in the mass accretion rate onto the compact object due to a decrease in the mass-loss rate from the primary.

MAGIC TeV Gamma-Ray Observations of Markarian 421 during Multiwavelength Campaigns in 2006

Wide-range spectral coverage of blazar-type active galactic nuclei is of paramount importance for understanding the particle acceleration mechanisms assumed to take place in their jets. The Major Atmospheric Gamma Imaging Cerenkov (MAGIC) telescope participated in three multiwavelength (MWL) campaigns, observing the blazar Markarian (Mkn) 421 during the nights of April 28 and 29, 2006, and June 14, 2006. Aims. We analyzed the corresponding MAGIC very-high energy observations during 9 nights from April 22 to 30, 2006 and on June 14, 2006. We inferred light curves with sub-day resolution and night-by-night energy spectra. Methods. MAGIC detects γ-rays by observing extended air showers in the atmosphere. The obtained air-shower images were analyzed using the standard MAGIC analysis chain. Results. A strong γ-ray signal was detected from Mkn 421 on all observation nights. The flux (E > 250 GeV) varied on night-by-night basis between (0.92±0.11) × 10-10 cm-2 s-1 (0.57 Crab units) and (3.21±0.15) × 10-10 cm-2 s-1 (2.0 Crab units) in April 2006. There is a clear indication for intra-night variability with a doubling time of 36± min on the night of April 29, 2006, establishing once more rapid flux variability for this object. For all individual nights γ-ray spectra could be inferred, with power-law indices ranging from 1.66 to 2.47. We did not find statistically significant correlations between the spectral index and the flux state for individual nights. During the June 2006 campaign, a flux substantially lower than the one measured by the Whipple 10-m telescope four days later was found. Using a log-parabolic power law fit we deduced for some data sets the location of the spectral peak in the very-high energy regime. Our results confirm the indications of rising peak energy with increasing flux, as expected in leptonic acceleration models.

Monotonic continuous-time random walks with drift and stochastic reset events

In this paper we consider a stochastic process that may experience random reset events which suddenly bring the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonic continuous-time random walks with a constant drift: The process increases between the reset events, either by the effect of the random jumps, or by the action of the deterministic drift. As a result of all these combined factors interesting properties emerge, like the existence (for any drift strength) of a stationary transition probability density function, or the faculty of the model to reproduce power-law-like behavior. General formulas for two extreme statistics, the survival probability, and the mean exit time, are also derived. To corroborate in an independent way the results of the paper, Monte Carlo methods were used. These numerical estimations are in full agreement with the analytical predictions.

Cosmological networks

Networks often represent systems that do not have a long history of study in traditional fields of physics; albeit, there are some notable exceptions, such as energy landscapes and quantum gravity. Here, we consider networks that naturally arise in cosmology. Nodes in these networks are stationary observers uniformly distributed in an expanding open Friedmann-Lemaitre-Robertson-Walker universe with any scale factor and two observers are connected if one can causally influence the other. We show that these networks are growing Lorentz-invariant graphs with power-law distributions of node degrees. These networks encode maximum information about the observable universe available to a given observer.