A GRADIENT-LIKE NONAUTONOMOUS EVOLUTION PROCESS

In this paper we consider a dissipative damped wave equation with nonautonomous damping of the form u(tt) + beta(t)u(t) - Delta u + f(u) (1) in a bounded smooth domain Omega subset of R(n) with Dirichlet boundary conditions, where f is a dissipative smooth nonlinearity and the damping beta : R -> (0, infinity) is a suitable function. We prove, if (1) has finitely many equilibria, that all global bounded solutions of (1) are backwards and forwards asymptotic to equilibria. Thus, we give a class of examples of nonautonomous evolution processes for which the structure of the pullback attractors is well understood. That complements the results of [Carvalho & Langa, 2009] on characterization of attractors, where it was shown that a small nonautonomous perturbation of an autonomous gradient-like evolution process is also gradient-like. Note that the evolution process associated to (1) is not a small nonautonomous perturbation of any autonomous gradient-like evolution processes. Moreover, we are also able to prove that the pullback attractor for (1) is also a forwards attractor and that the rate of attraction is exponential.

UNIFORM DISSIPATIVENESS, ROBUST SYNCHRONIZATION AND LOCATION OF THE ATTRACTOR OF PARAMETRIZED NONAUTONOMOUS DISCRETE SYSTEMS

In this series of papers, we study issues related to the synchronization of two coupled chaotic discrete systems arising from secured communication. The first part deals with uniform dissipativeness with respect to parameter variation via the Liapunov direct method. We obtain uniform estimates of the global attractor for a general discrete nonautonomous system, that yields a uniform invariance principle in the autonomous case. The Liapunov function is allowed to have positive derivative along solutions of the system inside a bounded set, and this reduces substantially the difficulty of constructing a Liapunov function for a given system. In particular, we develop an approach that incorporates the classical Lagrange multiplier into the Liapunov function method to naturally extend those Liapunov functions from continuous dynamical system to their discretizations, so that the corresponding uniform dispativeness results are valid when the step size of the discretization is small. Applications to the discretized Lorenz system and the discretization of a time-periodic chaotic system are given to illustrate the general results. We also show how to obtain uniform estimation of attractors for parametrized linear stable systems with nonlinear perturbation.

Fractal structures in nonlinear plasma physics

Fractal structures appear in many situations related to the dynamics of conservative as well as dissipative dynamical systems, being a manifestation of chaotic behaviour. In open area-preserving discrete dynamical systems we can find fractal structures in the form of fractal boundaries, associated to escape basins, and even possessing the more general property of Wada. Such systems appear in certain applications in plasma physics, like the magnetic field line behaviour in tokamaks with ergodic limiters. The main purpose of this paper is to show how such fractal structures have observable consequences in terms of the transport properties in the plasma edge of tokamaks, some of which have been experimentally verified. We emphasize the role of the fractal structures in the understanding of mesoscale phenomena in plasmas, such as electromagnetic turbulence.

Rainforest Aerosols as Biogenic Nuclei of Clouds and Precipitation in the Amazon

The Amazon is one of the few continental regions where atmospheric aerosol particles and their effects on climate are not dominated by anthropogenic sources. During the wet season, the ambient conditions approach those of the pristine pre-industrial era. We show that the fine submicrometer particles accounting for most cloud condensation nuclei are predominantly composed of secondary organic material formed by oxidation of gaseous biogenic precursors. Supermicrometer particles, which are relevant as ice nuclei, consist mostly of primary biological material directly released from rainforest biota. The Amazon Basin appears to be a biogeochemical reactor, in which the biosphere and atmospheric photochemistry produce nuclei for clouds and precipitation sustaining the hydrological cycle. The prevailing regime of aerosol-cloud interactions in this natural environment is distinctly different from polluted regions.

Mechanical analysis of infant carrying in hominoids

In all higher nonhuman primates, species survival depends upon safe carrying of infants clinging to body hair of adults. In this work, measurements of mechanical properties of ape hair (gibbon, orangutan, and gorilla) are presented, focusing on constraints for safe infant carrying. Results of hair tensile properties are shown to be species-dependent. Analysis of the mechanics of the mounting position, typical of heavier infant carrying among African apes, shows that both clinging and friction are necessary to carry heavy infants. As a consequence, a required relationship between infant weight, hair-hair friction coefficient, and body angle exists. The hair-hair friction coefficient is measured using natural ape skin samples, and dependence on load and humidity is analyzed. Numerical evaluation of the equilibrium constraint is in agreement with the knuckle-walking quadruped position of African apes. Bipedality is clearly incompatible with the usual clinging and mounting pattern of infant carrying, requiring a revision of models of hominization in relation to the divergence between apes and hominins. These results suggest that safe carrying of heavy infants justify the emergence of biped form of locomotion. Ways to test this possibility are foreseen here.

Low-dimensional chaos and wave turbulence in plasmas

We investigated drift-wave turbulence in the plasma edge of a small tokamak by considering solutions of the Hasegawa-Mima equation involving three interacting modes in Fourier space. The resulting low-dimensional dynamics presented periodic as well as chaotic evolution of the Fourier-mode amplitudes, and we performed the control of chaotic behaviour through the application of a fourth resonant wave of small amplitude.

Biomechanical effects of environmental and engineered particles on human airway smooth muscle cells

The past decade has seen significant increases in combustion-generated ambient particles, which contain a nanosized fraction (less than 100 nm), and even greater increases have occurred in engineered nanoparticles (NPs) propelled by the booming nanotechnology industry. Although inhalation of these particulates has become a public health concern, human health effects and mechanisms of action for NPs are not well understood. Focusing on the human airway smooth muscle cell, here we show that the cellular mechanical function is altered by particulate exposure in a manner that is dependent upon particle material, size and dose. We used Alamar Blue assay to measure cell viability and optical magnetic twisting cytometry to measure cell stiffness and agonist-induced contractility. The eight particle species fell into four categories, based on their respective effect on cell viability and on mechanical function. Cell viability was impaired and cell contractility was decreased by (i) zinc oxide (40-100 nm and less than 44 mu m) and copper(II) oxide (less than 50 nm); cell contractility was decreased by (ii) fluorescent polystyrene spheres (40 nm), increased by (iii) welding fumes and unchanged by (iv) diesel exhaust particles, titanium dioxide (25 nm) and copper(II) oxide (less than 5 mu m), although in none of these cases was cell viability impaired. Treatment with hydrogen peroxide up to 500 mu M did not alter viability or cell mechanics, suggesting that the particle effects are unlikely to be mediated by particle-generated reactive oxygen species. Our results highlight the susceptibility of cellular mechanical function to particulate exposures and suggest that direct exposure of the airway smooth muscle cells to particulates may initiate or aggravate respiratory diseases.

CRITICAL BEHAVIOR AND THRESHOLD OF COEXISTENCE OF A PREDATOR-PREY STOCHASTIC MODEL IN A 2D LATTICE

We investigate the critical behavior of a stochastic lattice model describing a predator-prey system. By means of Monte Carlo procedure we simulate the model defined on a regular square lattice and determine the threshold of species coexistence, that is, the critical phase boundaries related to the transition between an active state, where both species coexist and an absorbing state where one of the species is extinct. A finite size scaling analysis is employed to determine the order parameter, order parameter fluctuations, correlation length and the critical exponents. Our numerical results for the critical exponents agree with those of the directed percolation universality class. We also check the validity of the hyperscaling relation and present the data collapse curves.

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.

Observation of an Antimatter Hypernucleus

Nuclear collisions recreate conditions in the universe microseconds after the Big Bang. Only a very small fraction of the emitted fragments are light nuclei, but these states are of fundamental interest. We report the observation of antihypertritons-comprising an antiproton, an antineutron, and an antilambda hyperon-produced by colliding gold nuclei at high energy. Our analysis yields 70 +/- 17 antihypertritons (3/Lambda(H) over bar) and 157 +/- 30 hypertritons ((3)(Lambda)H). The measured yields of (3)(Lambda)H (3/Lambda(H) over bar) and (3)He ((3)(He) over bar) are similar, suggesting an equilibrium in coordinate and momentum space populations of up, down, and strange quarks and antiquarks, unlike the pattern observed at lower collision energies. The production and properties of antinuclei, and of nuclei containing strange quarks, have implications spanning nuclear and particle physics, astrophysics, and cosmology.

Observation of the antimatter helium-4 nucleus

High-energy nuclear collisions create an energy density similar to that of the Universe microseconds after the Big Bang(1); in both cases, matter and antimatter are formed with comparable abundance. However, the relatively short-lived expansion in nuclear collisions allows antimatter to decouple quickly from matter, and avoid annihilation. Thus, a high-energy accelerator of heavy nuclei provides an efficient means of producing and studying antimatter. The antimatter helium-4 nucleus ((4)(He) over bar), also known as the anti-alpha ((alpha) over bar), consists of two antiprotons and two antineutrons (baryon number B = -4). It has not been observed previously, although the alpha-particle was identified a century ago by Rutherford and is present in cosmic radiation at the ten per cent level(2). Antimatter nuclei with B -1 have been observed only as rare products of interactions at particle accelerators, where the rate of antinucleus production in high-energy collisions decreases by a factor of about 1,000 with each additional antinucleon(3-5). Here we report the observation of (4)<(He) over bar, the heaviest observed antinucleus to date. In total, 18 (4)(He) over bar counts were detected at the STAR experiment at the Relativistic Heavy Ion Collider (RHIC; ref. 6) in 10(9) recorded gold-on-gold (Au+Au) collisions at centre-of-mass energies of 200 GeV and 62 GeV per nucleon-nucleon pair. The yield is consistent with expectations from thermodynamic(7) and coalescent nucleosynthesis(8) models, providing an indication of the production rate of even heavier antimatter nuclei and a benchmark for possible future observations of (4)(He) over bar in cosmic radiation.

Fractal structures in stenoses and aneurysms in blood vessels

Recent advances in the field of chaotic advection provide the impetus to revisit the dynamics of particles transported by blood flow in the presence of vessel wall irregularities. The irregularity, being either a narrowing or expansion of the vessel, mimicking stenoses or aneurysms, generates abnormal flow patterns that lead to a peculiar filamentary distribution of advected particles, which, in the blood, would include platelets. Using a simple model, we show how the filamentary distribution depends on the size of the vessel wall irregularity, and how it varies under resting or exercise conditions. The particles transported by blood flow that spend a long time around a disturbance either stick to the vessel wall or reside on fractal filaments. We show that the faster flow associated with exercise creates widespread filaments where particles can get trapped for a longer time, thus allowing for the possible activation of such particles. We argue, based on previous results in the field of active processes in flows, that the non-trivial long-time distribution of transported particles has the potential to have major effects on biochemical processes occurring in blood flow, including the activation and deposition of platelets. One aspect of the generality of our approach is that it also applies to other relevant biological processes, an example being the coexistence of plankton species investigated previously.

Three-Color Entanglement

Entanglement is an essential quantum resource for the acceleration of information processing as well as for sophisticated quantum communication protocols. Quantum information networks are expected to convey information from one place to another by using entangled light beams. We demonstrated the generation of entanglement among three bright beams of light, all of different wavelengths (532.251, 1062.102, and 1066.915 nanometers). We also observed disentanglement for finite channel losses, the continuous variable counterpart to entanglement sudden death.

MODELING THE EVOLUTION OF COMPLEX NETWORKS THROUGH THE PATH-STAR TRANSFORMATION AND OPTIMAL MULTIVARIATE METHODS

The topology of real-world complex networks, such as in transportation and communication, is always changing with time. Such changes can arise not only as a natural consequence of their growth, but also due to major modi. cations in their intrinsic organization. For instance, the network of transportation routes between cities and towns ( hence locations) of a given country undergo a major change with the progressive implementation of commercial air transportation. While the locations could be originally interconnected through highways ( paths, giving rise to geographical networks), transportation between those sites progressively shifted or was complemented by air transportation, with scale free characteristics. In the present work we introduce the path-star transformation ( in its uniform and preferential versions) as a means to model such network transformations where paths give rise to stars of connectivity. It is also shown, through optimal multivariate statistical methods (i.e. canonical projections and maximum likelihood classification) that while the US highways network adheres closely to a geographical network model, its path-star transformation yields a network whose topological properties closely resembles those of the respective airport transportation network.

Epidemics in networks of spatially correlated three-dimensional root-branching structures

Using digitized images of the three-dimensional, branching structures for root systems of bean seedlings, together with analytical and numerical methods that map a common susceptible-infected- recovered (`SIR`) epidemiological model onto the bond percolation problem, we show how the spatially correlated branching structures of plant roots affect transmission efficiencies, and hence the invasion criterion, for a soil-borne pathogen as it spreads through ensembles of morphologically complex hosts. We conclude that the inherent heterogeneities in transmissibilities arising from correlations in the degrees of overlap between neighbouring plants render a population of root systems less susceptible to epidemic invasion than a corresponding homogeneous system. Several components of morphological complexity are analysed that contribute to disorder and heterogeneities in the transmissibility of infection. Anisotropy in root shape is shown to increase resilience to epidemic invasion, while increasing the degree of branching enhances the spread of epidemics in the population of roots. Some extension of the methods for other epidemiological systems are discussed.