A scenario for torus T(2) destruction via a global bifurcation

We show a scenario of a two-frequeney torus breakdown, in which a global bifurcation occurs due to the collision of a quasi-periodic torus T(2) with saddle points, creating a heteroclinic saddle connection. We analyze the geometry of this torus-saddle collision by showing the local dynamics and the invariant manifolds (global dynamics) of the saddle points. Moreover, we present detailed evidences of a heteroclinic saddle-focus orbit responsible for the type-if intermittency induced by this global bifurcation. We also characterize this transition to chaos by measuring the Lyapunov exponents and the scaling laws. (C) 2007 Elsevier Ltd. All rights reserved.

Dynamic portrait of the planetary 2/1 mean-motion resonance - II. Systems with a more massive inner planet

This paper presents the second part in our study of the global structure of the planar phase space of the planetary three-body problem, when both planets lie in the vicinity of a 2/1 mean-motion resonance. While Paper I was devoted to cases where the outer planet is the more massive body, the present work is devoted to the cases where the more massive body is the inner planet. As before, outside the well-known Apsidal Corotation Resonances (ACR), the phase space shows a complex picture marked by the presence of several distinct regimes of resonant and non-resonant motion, crossed by families of periodic orbits and separated by chaotic zones. When the chosen values of the integrals of motion lead to symmetric ACR, the global dynamics are generally similar to the structure presented in Paper I. However, for asymmetric ACR the resonant phase space is strikingly different and shows a galore of distinct dynamical states. This structure is shown with the help of dynamical maps constructed on two different representative planes, one centred on the unstable symmetric ACR and the other on the stable asymmetric equilibrium solution. Although the study described in the work may be applied to any mass ratio, we present a detailed analysis for mass values similar to the Jupiter-Saturn case. Results give a global view of the different dynamical states available to resonant planets with these characteristics. Some of these dynamical paths could have marked the evolution of the giant planets of our Solar system, assuming they suffered a temporary capture in the 2/1 resonance during the latest stages of the formation of our Solar system.

IPCC global coupled model simulations of the South America monsoon system

This study examines the variability of the South America monsoon system (SAMS) over tropical South America (SA). The onset, end, and total rainfall during the summer monsoon are investigated using precipitation pentad estimates from the global precipitation climatology project (GPCP) 1979-2006. Likewise, the variability of SAMS characteristics is examined in ten Intergovernmental Panel on Climate Change (IPCC) global coupled climate models in the twentieth century (1981-2000) and in a future scenario of global change (A1B) (2081-2100). It is shown that most IPCC models misrepresent the intertropical convergence zone and therefore do not capture the actual annual cycle of precipitation over the Amazon and northwest SA. Most models can correctly represent the spatiotemporal variability of the annual cycle of precipitation in central and eastern Brazil such as the correct phase of dry and wet seasons, onset dates, duration of rainy season and total accumulated precipitation during the summer monsoon for the twentieth century runs. Nevertheless, poor representation of the total monsoonal precipitation over the Amazon and northeast Brazil is observed in a large majority of the models. Overall, MI-ROC3.2-hires, MIROC3.2-medres and MRI-CGCM3.2.3 show the most realistic representation of SAMS`s characteristics such as onset, duration, total monsoonal precipitation, and its interannual variability. On the other hand, ECHAM5, GFDL-CM2.0 and GFDL-CM2.1 have the least realistic representation of the same characteristics. For the A1B scenario the most coherent feature observed in the IPCC models is a reduction in precipitation over central-eastern Brazil during the summer monsoon, comparatively with the present climate. The IPCC models do not indicate statistically significant changes in SAMS onset and demise dates for the same scenario.

Global properties of `ordinary` early-type galaxies: photometry and spectroscopy of stars and globular clusters in NGC 4494

We present a comprehensive analysis of the spatial, kinematic and chemical properties of stars and globular clusters (GCs) in the `ordinary` elliptical galaxy NGC 4494 using data from the Keck and Subaru telescopes. We derive galaxy surface brightness and colour profiles out to large galactocentric radii. We compare the latter to metallicities derived using the near-infrared Calcium Triplet. We obtain stellar kinematics out to similar to 3.5 effective radii. The latter appear flattened or elongated beyond similar to 1.8 effective radii in contrast to the relatively round photometric isophotes. In fact, NGC 4494 may be a flattened galaxy, possibly even an S0, seen at an inclination of similar to 45 degrees. We publish a catalogue of 431 GC candidates brighter than i(0) = 24 based on the photometry, of which 109 are confirmed spectroscopically and 54 have measured spectroscopic metallicities. We also report the discovery of three spectroscopically confirmed ultra-compact dwarfs around NGC 4494 with measured metallicities of -0.4 less than or similar to [Fe/H] less than or similar to -0.3. Based on their properties, we conclude that they are simply bright GCs. The metal-poor GCs are found to be rotating with similar amplitude as the galaxy stars, while the metal-rich GCs show marginal rotation. We supplement our analysis with available literature data and results. Using model predictions of galaxy formation, and a suite of merger simulations, we find that many of the observational properties of NGC 4494 may be explained by formation in a relatively recent gas-rich major merger. Complete studies of individual galaxies incorporating a range of observational avenues and methods such as the one presented here will be an invaluable tool for constraining the fine details of galaxy formation models, especially at large galactocentric radii.

Araucaria forest dynamics in relation to fire frequency in southern Brazil based on fossil and modern pollen dataf

To elucidate the relationship between forest dynamics and fire frequency pollen percentages and charcoal amounts from a 120 cm long peat core and from samples of modern pollen rain were collected along a transect. The study site in southern Brazil is characterized by a species-rich mosaic of grassland-Araucaria forest. It is of crucial importance for management strategies for conservation to understand the development and maintenance of these vegetation mosaics including their sharp forest-grassland boundaries. During the late Holocene, considerable changes occurred in the area. From Anno Domini (AD) 1360 to 1410, the area was dominated by Campos (grassland) vegetation and fire was very common. From AD 1410 to 1500, Araucaria forest expanded and fire was less frequent. From AD 1500 to 1580, Campos grassland spread and the Araucaria forest ceased its development, apparently due to the increase of fire. From AD 1580 to 1935, after a decrease in fire frequency, Araucaria forest expanded again. From AD 1935 to the present, the Araucaria forest expanded while the Campos area decreased. Fire was very rare in this period. The results indicate a strong interaction of forest expansion, forming a mosaic of Campos and Araucaria forest, and the frequency of fire during the past 600 years. A possible collapse of the indigenous population following the post-Colombian colonization in southern Brazil after about AD 1550 may have caused a great reduction of fire frequency. The introduction of cattle (probably after AD 1780) and the resulting decrease of fire frequency might be the reason for forest expansion. Fire is probably the most important factor controlling the dynamics of the forest-grassland mosaics and the formation of sharp borders between these two vegetation types. (C) 2010 Elsevier B.V. All rights reserved.

Dynamics of the viscous Cahn-Hilliard equation

We study generalized viscous Cahn-Hilliard problems with nonlinearities satisfying critical growth conditions in W-0(1,p)(Omega), where Omega is a bounded smooth domain in R-n, n >= 3. In the critical growth case, we prove that the problems are locally well posed and obtain a bootstrapping procedure showing that the solutions are classical. For p = 2 and almost critical dissipative nonlinearities we prove global well posedness, existence of global attractors in H-0(1)(Omega) and, uniformly with respect to the viscosity parameter, L-infinity(Omega) bounds for the attractors. Finally, we obtain a result on continuity of regular attractors which shows that, if n = 3, 4, the attractor of the Cahn-Hilliard problem coincides (in a sense to be specified) with the attractor for the corresponding semilinear heat equation. (C) 2008 Elsevier Inc. All rights reserved.

Dynamics of a class of ODEs more general than almost periodic

A temporally global solution, if it exists, of a nonautonomous ordinary differential equation need not be periodic, almost periodic or almost automorphic when the forcing term is periodic, almost periodic or almost automorphic, respectively. An alternative class of functions extending periodic and almost periodic functions which has the property that a bounded temporally global solution solution of a nonautonomous ordinary differential equation belongs to this class when the forcing term does is introduced here. Specifically, the class of functions consists of uniformly continuous functions, defined on the real line and taking values in a Banach space, which have pre-compact ranges. Besides periodic and almost periodic functions, this class also includes many nonrecurrent functions. Assuming a hyperbolic structure for the unperturbed linear equation and certain properties for the linear and nonlinear parts, the existence of a special bounded entire solution, as well the existence of stable and unstable manifolds of this solution are established. Moreover, it is shown that this solution and these manifolds inherit the temporal behaviour of the vector field equation. In the stable case it is shown that this special solution is the pullback attractor of the system. A class of infinite dimensional examples involving a linear operator consisting of a time independent part which generates a C(0)-semigroup plus a small time dependent part is presented and applied to systems of coupled heat and beam equations. (C) 2010 Elsevier Ltd. All rights reserved.

Combining structure and dynamics: non-denaturing high-pressure effect on lysozyme in solution

Small-angle X-ray scattering (SAXS) and elastic and quasi-elastic neutron scattering techniques were used to investigate the high-pressure-induced changes on interactions, the low-resolution structure and the dynamics of lysozyme in solution. SAXS data, analysed using a global-fit procedure based on a new approach for hydrated protein form factor description, indicate that lysozyme completely maintains its globular structure up to 1500 bar, but significant modi. cations in the protein-protein interaction potential occur at approximately 600-1000 bar. Moreover, the mass density of the protein hydration water shows a clear discontinuity within this pressure range. Neutron scattering experiments indicate that the global and the local lysozyme dynamics change at a similar threshold pressure. A clear evolution of the internal protein dynamics from diffusing to more localized motions has also been probed. Protein structure and dynamics results have then been discussed in the context of protein-water interface and hydration water dynamics. According to SAXS results, the new configuration of water in the first hydration layer induced by pressure is suggested to be at the origin of the observed local mobility changes.

Opinion dynamics of learning agents: does seeking consensus lead to disagreement?

We study opinion dynamics in a population of interacting adaptive agents voting on a set of issues represented by vectors. We consider agents who can classify issues into one of two categories and can arrive at their opinions using an adaptive algorithm. Adaptation comes from learning and the information for the learning process comes from interacting with other neighboring agents and trying to change the internal state in order to concur with their opinions. The change in the internal state is driven by the information contained in the issue and in the opinion of the other agent. We present results in a simple yet rich context where each agent uses a Boolean perceptron to state their opinion. If the update occurs with information asynchronously exchanged among pairs of agents, then the typical case, if the number of issues is kept small, is the evolution into a society torn by the emergence of factions with extreme opposite beliefs. This occurs even when seeking consensus with agents with opposite opinions. If the number of issues is large, the dynamics becomes trapped, the society does not evolve into factions and a distribution of moderate opinions is observed. The synchronous case is technically simpler and is studied by formulating the problem in terms of differential equations that describe the evolution of order parameters that measure the consensus between pairs of agents. We show that for a large number of issues and unidirectional information flow, global consensus is a fixed point; however, the approach to this consensus is glassy for large societies.

Beyond the average: Detecting global singular nodes from local features in complex networks

Deviations from the average can provide valuable insights about the organization of natural systems. The present article extends this important principle to the systematic identification and analysis of singular motifs in complex networks. Six measurements quantifying different and complementary features of the connectivity around each node of a network were calculated, and multivariate statistical methods applied to identify singular nodes. The potential of the presented concepts and methodology was illustrated with respect to different types of complex real-world networks, namely the US air transportation network, the protein-protein interactions of the yeast Saccharomyces cerevisiae and the Roget thesaurus networks. The obtained singular motifs possessed unique functional roles in the networks. Three classic theoretical network models were also investigated, with the Barabasi-Albert model resulting in singular motifs corresponding to hubs, confirming the potential of the approach. Interestingly, the number of different types of singular node motifs as well as the number of their instances were found to be considerably higher in the real-world networks than in any of the benchmark networks. Copyright (C) EPLA, 2009