An estimate on the fractal dimension of attractors of gradient-like dynamical systems

This paper is dedicated to estimate the fractal dimension of exponential global attractors of some generalized gradient-like semigroups in a general Banach space in terms of the maximum of the dimension of the local unstable manifolds of the isolated invariant sets, Lipschitz properties of the semigroup and the rate of exponential attraction. We also generalize this result for some special evolution processes, introducing a concept of Morse decomposition with pullback attractivity. Under suitable assumptions, if (A, A*) is an attractor-repeller pair for the attractor A of a semigroup {T(t) : t >= 0}, then the fractal dimension of A can be estimated in terms of the fractal dimension of the local unstable manifold of A*, the fractal dimension of A, the Lipschitz properties of the semigroup and the rate of the exponential attraction. The ingredients of the proof are the notion of generalized gradient-like semigroups and their regular attractors, Morse decomposition and a fine analysis of the structure of the attractors. As we said previously, we generalize this result for some evolution processes using the same basic ideas. (C) 2012 Elsevier Ltd. All rights reserved.

STRUCTURE AND BIFURCATION OF PULLBACK ATTRACTORS IN A NON-AUTONOMOUS CHAFEE-INFANTE EQUATION

The Chafee-Infante equation is one of the canonical infinite-dimensional dynamical systems for which a complete description of the global attractor is available. In this paper we study the structure of the pullback attractor for a non-autonomous version of this equation, u(t) = u(xx) + lambda(xx) - lambda u beta(t)u(3), and investigate the bifurcations that this attractor undergoes as A is varied. We are able to describe these in some detail, despite the fact that our model is truly non-autonomous; i.e., we do not restrict to 'small perturbations' of the autonomous case.

Multi-strange baryon production in pp collisions at root s=7 TeV with ALICE

A measurement of the multi-strange Xi(-) and Omega(-) baryons and their antiparticles by the ALICE experiment at the CERN Large Hadron Collider (LHC) is presented for inelastic proton-proton collisions at a centre-of-mass energy of 7 TeV. The transverse momentum (p(T)) distributions were studied at mid-rapidity (vertical bar y vertical bar < 0.5) in the range of 0.6 < p(T) < 8.5 GeV/c Xi(-) for and Xi(+) baryons, and in the range of 0.8 < P-T < 5 GeV/c for Omega(-) and<(Omega)over bar>(+). Baryons and antibaryons were measured as separate particles and we find that the baryon to antibaryon ratio of both particle species is consistent with unity over the entire range of the measurement. The statistical precision of the current data has allowed us to measure a difference between the mean p(T) of Xi(-) ((Xi) over bar)(+) and Omega(-) ((Omega) over bar (+)). Particle yields, mean pi, and the spectra in the intermediate pi range are not well described by the PYTHIA Perugia 2011 tune Monte Carlo event generator, which has been tuned to reproduce the early LHC data. The discrepancy is largest for Omega(-)((Omega) over bar (+)). This PYTHIA tune approaches the pi spectra of Xi(-) and Xi(+) baryons below p(T) <0.85 GeV/c and describes the Xi(-) and Xi(+) spectra above p(T) > 6.0 GeV/c. We also illustrate the difference between the experimental data and model by comparing the corresponding ratios of (Omega(-) +(Omega) over bar (+))/(Xi(-) + Xi(+)) as a function of transverse mass. (C) 2012 CERN. Published by Elsevier B.V. All rights reserved.

Pullback exponential attractors for evolution processes in Banach spaces: properties and applications

This article is a continuation of our previous work [5], where we formulated general existence theorems for pullback exponential attractors for asymptotically compact evolution processes in Banach spaces and discussed its implications in the autonomous case. We now study properties of the attractors and use our theoretical results to prove the existence of pullback exponential attractors in two examples, where previous results do not apply.

Bakhtin e o grupo: incongruências de uma linguística ortodoxa

For these Russian authors, a sign has to be faithful to reality but what is, in fact, «to be faithful», what is «reality»? They suggest that thought structures itself only by means of signs – as Peirce, who denies the reality of dreams saying that the act to feel hunger is an ideological expression and the shouts of a new-born are already appreciative manifestations of this new human being. The authors had inspired the structuralism, saying that a «semiodiscourse» structures men. Although this instance, word remains neutral, assertion strange to their Hegelian and Marxist roots; their paradigm in contrast, can be Heideggerian, according to which, only the «marked» being exists: looking at one determined thing, I place it, I fit it in its context. To place something is to attribute sense and that is more Stoic than, in fact, Marxist.

An extension of the invariance principle for dwell-time switched nonlinear systems

In this paper, we propose an extension of the invariance principle for nonlinear switched systems under dwell-time switched solutions. This extension allows the derivative of an auxiliary function V, also called a Lyapunov-like function, along the solutions of the switched system to be positive on some sets. The results of this paper are useful to estimate attractors of nonlinear switched systems and corresponding basins of attraction. Uniform estimates of attractors and basin of attractions with respect to time-invariant uncertain parameters are also obtained. Results for a common Lyapunov-like function and multiple Lyapunov-like functions are given. Illustrative examples show the potential of the theoretical results in providing information on the asymptotic behavior of nonlinear dynamical switched systems. (C) 2012 Elsevier B.V. All rights reserved.

Continuity of Dynamical Structures for Nonautonomous Evolution Equations Under Singular Perturbations

In this paper we study the continuity of invariant sets for nonautonomous infinite-dimensional dynamical systems under singular perturbations. We extend the existing results on lower-semicontinuity of attractors of autonomous and nonautonomous dynamical systems. This is accomplished through a detailed analysis of the structure of the invariant sets and its behavior under perturbation. We prove that a bounded hyperbolic global solutions persists under singular perturbations and that their nonlinear unstable manifold behave continuously. To accomplish this, we need to establish results on roughness of exponential dichotomies under these singular perturbations. Our results imply that, if the limiting pullback attractor of a nonautonomous dynamical system is the closure of a countable union of unstable manifolds of global bounded hyperbolic solutions, then it behaves continuously (upper and lower) under singular perturbations.

Delay nonlinear boundary conditions as limit of reactions concentrating in the boundary

In this work, we are interested in the dynamic behavior of a parabolic problem with nonlinear boundary conditions and delay in the boundary. We construct a reaction-diffusion problem with delay in the interior, where the reaction term is concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary, as a parameter epsilon goes to zero. We analyze the limit of the solutions of this concentrated problem and prove that these solutions converge in certain continuous function spaces to the unique solution of the parabolic problem with delay in the boundary. This convergence result allows us to approximate the solution of equations with delay acting on the boundary by solutions of equations with delay acting in the interior and it may contribute to analyze the dynamic behavior of delay equations when the delay is at the boundary. (C) 2012 Elsevier Inc. All rights reserved.

Strangeness Enhancement in Cu-Cu and Au-Au Collisions at root s(NN)=200 GeV

We report new STAR measurements of midrapidity yields for the Lambda, (Lambda) over bar, K-S(0), Xi(-), (Xi) over bar (+), Omega(-), (Omega) over bar (+) particles in Cu + Cu collisions at root s(NN) = 200 GeV, and midrapidity yields for the Lambda, (Lambda) over bar, K-S(0) particles in Au + Au at root s(NN) = 200 GeV. We show that, at a given number of participating nucleons, the production of strange hadrons is higher in Cu + Cu collisions than in Au + Au collisions at the same center-of-mass energy. We find that aspects of the enhancement factors for all particles can be described by a parametrization based on the fraction of participants that undergo multiple collisions.

The nature of the companion of PSR J1719-1438: a white dwarf or an exotic object?

We raise the possibility that the very dense, compact companion of PSR J1719-1438, which has a Jupiter-like mass, is an exotic quark object rather than a light helium or carbon white dwarf. The exotic hypothesis naturally explains some of the observed features, and provides quite strong predictions for this system, to be confirmed or refuted in feasible future studies.

Decay of energy and suppression of Fermi acceleration in a dissipative driven stadium-like billiard

The behavior of the average energy for an ensemble of non-interacting particles is studied using scaling arguments in a dissipative time-dependent stadium-like billiard. The dynamics of the system is described by a four dimensional nonlinear mapping. The dissipation is introduced via inelastic collisions between the particles and the moving boundary. For different combinations of initial velocities and damping coefficients, the long time dynamics of the particles leads them to reach different states of final energy and to visit different attractors, which change as the dissipation is varied. The decay of the average energy of the particles, which is observed for a large range of restitution coefficients and different initial velocities, is described using scaling arguments. Since this system exhibits unlimited energy growth in the absence of dissipation, our results for the dissipative case give support to the principle that Fermi acceleration seems not to be a robust phenomenon. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3699465]

Mutual Information Rate and Bounds for It

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two time series (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators.

Entropy, complexity and disequilibrium in compact stars

We used the statistical measurements of information entropy, disequilibrium and complexity to infer a hierarchy of equations of state for two types of compact stars from the broad class of neutron stars, namely, with hadronic composition and with strange quark composition. Our results show that, since order costs energy. Nature would favor the exotic strange stars even though the question of how to form the strange stars cannot be answered within this approach. (C) 2012 Elsevier B.V. All rights reserved.

Production of K*(892)(0) and phi(1020) in pp collisions at root s=7 TeV

The production of K*(892)(0) and phi(1020) in pp collisions at root s = 7 TeV was measured by the ALICE experiment at the LHC. The yields and the transverse momentum spectra d(2)N/dydp(T) at midrapidity vertical bar y vertical bar < 0.5 in the range 0 < p(T) < 6 GeV/c for K*(892)(0) and 0.4 < p(T) < 6 GeV/c for phi(1020) are reported and compared to model predictions. Using the yield of pions, kaons, and Omega baryons measured previously by ALICE at root s = 7 TeV, the ratios K*/K-, phi/K*, phi/ K-, phi/pi(-), and (Omega + <(Omega)over bar>)/phi are presented. The values of the K*/K-, phi/K* and phi/K- ratios are similar to those found at lower centre-of-mass energies. In contrast, the phi/pi(-) ratio, which has been observed to increase with energy, seems to saturate above 200 GeV. The (Omega + (Omega) over bar)/phi ratio in the p(T) range 1-5 GeV/ c is found to be in good agreement with the prediction of the HIJING/B (B) over bar v2.0model with a strong colour field.

Remarks on Parametric Surface Waves in a Nonlinear and Non-Ideally Excited Tank

We studied free surface oscillations of a fluid in a cylinder tank excited by an electric motor with limited power supply. We investigated the possibility of parametric resonance in this system, showing that the excitation mechanism can generate chaotic response. Numerical experiments are carried out to present the existence of several types of regular and chaotic attractors. For the first time powers (power of the motor, power consumed by the damping force under fluid free surface oscillations, and a total power) are calculated, investigated, and shown for different regimes, regular and chaotic ones for parametric resonance interactions. [DOI: 10.1115/1.4005844]