Lower semicontinuity of attractors for non-autonomous dynamical systems

This paper is concerned with the lower semicontinuity of attractors for semilinear non-autonomous differential equations in Banach spaces. We require the unperturbed attractor to be given as the union of unstable manifolds of time-dependent hyperbolic solutions, generalizing previous results valid only for gradient-like systems in which the hyperbolic solutions are equilibria. The tools employed are a study of the continuity of the local unstable manifolds of the hyperbolic solutions and results on the continuity of the exponential dichotomy of the linearization around each of these solutions.

Regularity of solutions on the global attractor for a semilinear damped wave equation

We consider attractors A(eta), eta epsilon [0, 1], corresponding to a singularly perturbed damped wave equation u(tt) + 2 eta A(1/2)u(t) + au(t) + Au = f (u) in H-0(1)(Omega) x L-2 (Omega), where Omega is a bounded smooth domain in R-3. For dissipative nonlinearity f epsilon C-2(R, R) satisfying vertical bar f ``(s)vertical bar <= c(1 + vertical bar s vertical bar) with some c > 0, we prove that the family of attractors {A(eta), eta >= 0} is upper semicontinuous at eta = 0 in H1+s (Omega) x H-s (Omega) for any s epsilon (0, 1). For dissipative f epsilon C-3 (R, R) satisfying lim(vertical bar s vertical bar) (->) (infinity) f ``(s)/s = 0 we prove that the attractor A(0) for the damped wave equation u(tt) + au(t) + Au = f (u) (case eta = 0) is bounded in H-4(Omega) x H-3(Omega) and thus is compact in the Holder spaces C2+mu ((Omega) over bar) x C1+mu((Omega) over bar) for every mu epsilon (0, 1/2). As a consequence of the uniform bounds we obtain that the family of attractors {A(eta), eta epsilon [0, 1]} is upper and lower semicontinuous in C2+mu ((Omega) over bar) x C1+mu ((Omega) over bar) for every mu epsilon (0, 1/2). (c) 2007 Elsevier Inc. All rights reserved.

Continuity of attractors for parabolic problems with localized large diffusion

In this paper we study the continuity of asymptotics of semilinear parabolic problems of the form u(t) - div(p(x)del u) + lambda u =f(u) in a bounded smooth domain ohm subset of R `` with Dirichlet boundary conditions when the diffusion coefficient p becomes large in a subregion ohm(0) which is interior to the physical domain ohm. We prove, under suitable assumptions, that the family of attractors behave upper and lower semicontinuously as the diffusion blows up in ohm(0). (c) 2006 Elsevier Ltd. All rights reserved.

Dynamics in dumbbell domains III. Continuity of attractors

In this paper we conclude the analysis started in [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2006) 551-597] and continued in [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains II. The limiting problem, J. Differential Equations 247 (1) (2009) 174-202 (this issue)] concerning the behavior of the asymptotic dynamics of a dissipative reaction-diffusion equation in a dumbbell domain as the channel shrinks to a line segment. In [J.M. Arrieta, AN Carvalho. G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2006) 551-597], we have established an appropriate functional analytic framework to address this problem and we have shown the continuity of the set of equilibria. In [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz. Dynamics in dumbbell domains II. The limiting problem, J. Differential Equations 247 (1) (2009) 174-202 (this issue)], we have analyzed the behavior of the limiting problem. In this paper we show that the attractors are Upper semicontinuous and, moreover, if all equilibria of the limiting problem are hyperbolic, then they are lower semicontinuous and therefore, continuous. The continuity is obtained in L(p) and H(1) norms. (C) 2008 Elsevier Inc. All rights reserved.

On the continuity of pullback attractors for evolution processes

In this paper we give general results on the continuity of pullback attractors for nonlinear evolution processes. We then revisit results of [D. Li, P.E. Kloeden, Equi-attraction and the continuous dependence of pullback attractors on parameters, Stoch. Dyn. 4 (3) (2004) 373-384] which show that, under certain conditions, continuity is equivalent to uniformity of attraction over a range of parameters (""equi-attraction""): we are able to simplify their proofs and weaken the conditions required for this equivalence to hold. Generalizing a classical autonomous result [A.V. Babin, M.I. Vishik, Attractors of Evolution Equations, North Holland, Amsterdam, 1992] we give bounds on the rate of convergence of attractors when the family is uniformly exponentially attracting. To apply these results in a more concrete situation we show that a non-autonomous regular perturbation of a gradient-like system produces a family of pullback attractors that are uniformly exponentially attracting: these attractors are therefore continuous, and we can give an explicit bound on the distance between members of this family. (C) 2009 Elsevier Ltd. All rights reserved.

A non-autonomous strongly damped wave equation: Existence and continuity of the pullback attractor

In this paper we consider the strongly damped wave equation with time-dependent terms u(tt) - Delta u - gamma(t)Delta u(t) + beta(epsilon)(t)u(t) = f(u), in a bounded domain Omega subset of R(n), under some restrictions on beta(epsilon)(t), gamma(t) and growth restrictions on the nonlinear term f. The function beta(epsilon)(t) depends on a parameter epsilon, beta(epsilon)(t) -> 0. We will prove, under suitable assumptions, local and global well-posedness (using the uniform sectorial operators theory), the existence and regularity of pullback attractors {A(epsilon)(t) : t is an element of R}, uniform bounds for these pullback attractors, characterization of these pullback attractors and their upper and lower semicontinuity at epsilon = 0. (C) 2010 Elsevier Ltd. All rights reserved.

Semilinear parabolic problems in thin domains with a highly oscillatory boundary

In this paper, we study the behavior of the solutions of nonlinear parabolic problems posed in a domain that degenerates into a line segment (thin domain) which has an oscillating boundary. We combine methods from linear homogenization theory for reticulated structures and from the theory on nonlinear dynamics of dissipative systems to obtain the limit problem for the elliptic and parabolic problems and analyze the convergence properties of the solutions and attractors of the evolutionary equations. (C) 2011 Elsevier Ltd. All rights reserved.

CONTINUITY OF GLOBAL ATTRACTORS FOR A CLASS OF NON LOCAL EVOLUTION EQUATIONS

In this work we prove that the global attractors for the flow of the equation partial derivative m(r, t)/partial derivative t = -m(r, t) + g(beta J * m(r, t) + beta h), h, beta >= 0, are continuous with respect to the parameters h and beta if one assumes a property implying normal hyperbolicity for its (families of) equilibria.

Microbiological Shelf Life of Pasteurized Milk in Bottle and Pouch

Shelf life of pasteurized milk in Brazil ranges from 3 to 8 d, mainly due to poor cold chain conditions that prevail throughout the country and subject the product to repeated and/or severe temperature abuse. This study evaluated the influence of storage temperature on the microbiological stability of homogenized whole pasteurized milk (75 degrees C/15 s) packaged in high-density polyethylene (HDPE) bottle and low-density polyethylene (LDPE) pouch, both monolayer materials pigmented with titanium dioxide (TiO(2)). The storage temperatures investigated were 2, 4, 9, 14, and 16 degrees C. Microbiological evaluation was based on mesophilic and psychrotrophic counts with 7 log CFU/mL and 6 log CFU/mL, respectively, set as upper limits of acceptability for maintaining the quality of milk. The microbiological stability for pasteurized milk packaged in HDPE bottle and stored at 2, 4, 9, 14, and 16 degrees C was estimated at 43, 36, 8, 5, and 3 d, respectively. For milk samples packaged in LDPE pouch, shelf life was estimated at 37, 35, 7, 3, and 2 d, respectively. The determination of Q(10) and z values demonstrated that storage temperature has a greater influence on microbiological shelf life of pasteurized milk packaged in LDPE pouch compared to HDPE bottle. Based on the results of this study, HDPE bottle was better for storing pasteurized milk as compared to LDPE pouch.

Biogeography of Glandulocaudinae (Teleostei : Characiformes : Characidae) revisited: phylogenetic patterns, historical geology and genetic connectivity

The biogeography of the Glandulocaudinae ( former Glandulocaudini) is reviewed. The major pattern of diversification presented by this group of freshwater fishes can be clearly associated to the main aspects of the tectonic evolution of the southern portion of the Cis-Andean South American Platform. The phylogenetic relationships within the group suggest that the clade represented by Lophiobrycon is the sister-group of the more derived clade represented by the genus Glandulocauda and Mimagoniates. Lophiobrycon and Glandulocauda occur in areas of the ancient crystalline shield of southeastern Brazil and their present allopatric distribution is probably due to relict survival and tectonic vicariant events. Populations of Glandulocauda melanogenys are found in contiguous drainages in presently isolated upper parts of the Tiete, Guaratuba, Itatinga, and Ribeira de Iguape basins and this pattern of distribution is probably the result of river capture caused by tectonic processes that affected a large area in eastern and southeastern Brazil. The species of Mimagoniates are predominantly distributed along the eastern and southeastern coastal areas, but M. microlepis is additionally found in the rio Iguacu and Tibagi basins. Mimagoniates barberi occurs in both SW margin of the upper rio Parana basin and the lower Paraguay and Mimagoniates sp. occurs in the upper Paraguay river basin. Tectonic activations of the Continental Rift of Southeastern Brazil along the eastern margin of the Upper Parana basin promoted population fragmentation responsible of the present day distribution presented by Glandulocauda melanogenys. We hypothesize that occurrence of Mimagoniates along the lowland area around the Parana basin was due to a single or a multiple fragmentation of populations along the W-SW border of the upper Parana Basin, probably due to the major tectonic origin of the Chaco-Pantanal wetland foreland basins since the Miocene as well as Cenozoic tectonic activity along the borders of the upper Parana basin, such as in the eastern Paraguay, in the Asuncion Rift. Distributional pattern of Mimagoniates suggests that its initial diversification may be related to the tectonic evolution of the Chaco-Pantanal foreland basin system and a minimum age of 2.5 M.Y are proposed for this monophyletic group. Previous hypotheses on sea level fluctuations of the late Quaternary as being the main causal mechanism promoting cladogenesis and speciation of the group are critically reviewed. Phylogeographic studies based on molecular data indicate significant differences among the isolated populations of M. microlepis. These findings suggest that a much longer period of time and a paleogeographic landscape configuration of the Brazilian southeastern coastal region explain the present observed phylogenetic and biogeographic patterns.

A Survey of Fungal Contamination on Books in Public Libraries with Mechanical and Natural Ventilation

Libraries are very propitious environments for the growth of fungi. The great concentration of organic material available for these microorganisms, and often with the lack of adequate ventilation or climate control, would favour this situation. This study was conducted in 2003 to determine the predominant genera of fungi in public libraries by a survey of fungi contaminating the upper surface of books, with and without air conditioning in the city of Sao Paulo, Brazil, in the winter and summer, during the respective periods with high and low levels of airborne fungi in that city. Six libraries were chosen, located on the campus of the University of Sao Paulo, three of them with air conditioning and the other three with natural ventilation. In these six libraries, 31 genera of fungi were identified in total. The genera and frequency of contaminant fungi recovered differed significantly between the libraries with and without air conditioning and in the samples collected in the summer as opposed to the winter. Cladosporium was the most frequent in the libraries with and without air conditioning, and in the winter. Aspergillus was isolated more often in the summer.

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.

Study of metals transfer from environment using teeth as biomonitor

We investigated chronic incorporation of metals in individuals from poor families, living in a small, restrict and allegedly contaminated area in Sao Paulo city, the surroundings of the Guarapiranga dam, responsible for water supply to 25% of the city population. A total of 59 teeth from individuals 7 to 60 years old were collected. The average concentrations of Pb, Cd, Fe, Zn, Mn, Ni and Cr were determined with an Atomic Absorption Spectrophotometer. The concentrations of all metals as function of the individuals` age exhibited a remarkable similarity: peaks between 7 and 10 years and sharply decreasing at higher ages, which could be attributed to alimentary habits and persistence to metals exposure all along the individuals` life span. From all the measured metals, lead and cadmium were a matter of much more concern since their measured values are close to the upper limits of the world wide averages. (C) 2009 Elsevier Ltd. All rights reserved.

Geochemistry of iron and manganese in soils and sediments of a mangrove system, Island of Pai Matos (Cananeia - SP, Brazil)

Five zones along a transect of 180 m were selected for study on the Island of Pai Matos (Sao Paulo, Brazil). Four of the zones are colonised by vascular plants (Spartina SP, Laguncularia LG, Avicennia AV and Rhizophora RH) and were denominated soils, and the other zone, which lacks vegetation, was denominated sediment (SD). The geochemical conditions differed significantly in soils and sediment and also at different depths. The soils were oxic (Eh > 350 mV) or suboxic (Eh: 350-100 mV) at the surface and anoxic (Eh < 100 mV) at depth, whereas in the sediment anoxic conditions prevailed at all depths, but with a lower concentration of sulphides in the pore water and pyrite in the solid fraction. Under these geochemical conditions Fe is retained in the soils, while the Mn tends to be mobilized and lost. The most abundant form of iron oxyhydroxide was lepidocrocite (mean concentration for all sites and depths, 45 +/- 19 mu mol g(-1)), followed by goethite (30 19 mu mol g(-1))and ferrihydrite (19 +/- 11 mu mol g(-1)),with significant differences among the mean concentrations. There was a significant decrease with depth in all the types of Fe oxyhydroxides measured, particularly the poorly crystalline forms. The pyrite fraction was an important component of the free Fe pool (non-silicate Fe) in all soils as well as in the sediment, especially below 20 cm depth (mean concentration for all sites and depths, 60 +/- 54 mu mol CI). Furthermore, the mean concentration of Fe-pyrite for all sites and depths was higher than that obtained for any of the three Fe oxyhydroxides measured. The Fe-AVS was a minor fraction, indicating that the high concentrations of dissolved Fe in the soils in the upper area of the transect result from the oxidation of Fe sulphides during low tide. Mossbauer spectroscopy also revealed that most of the Fe (III) was associated with silicates, in this case nontronite. The presence of crystals of pyrite associated with phyllosilicates in samples from the upper layer of the soils may indicate that pyritization of this form of Fe(III) is more rapid than usually reported for ocean bed sediments. The sequential extraction of Mn did not reveal any clearly dominant fraction, with the Mn-carbonate fraction being the most prevalent, followed by exchangeable Mn and oxides of Mn, whereas pyrite-Mn and Mn associated with crystalline Fe-oxides were present at significantly lower concentrations. The high concentration of dissolved Mn found in the soils in the lower part of the transect is consistent with the fact that the solubility is determined by the carbonate fraction. Unlike for Fe, in the soils in the higher zone, which are subject to intense drainage during low tide, there was loss of Mn, as reflected by the concentration of total Mn. (C) 2008 Elsevier B.V. All rights reserved.

An inductor-free realization of the Chua`s circuit based on electronic analogy

Although literature presents several alternatives, an approach based on the electronic analogy was still not considered for the implementation of an inductor-free realization of the double scroll Chua`s circuit. This paper presents a new inductor-free configuration of the Chua`s circuit based on the electronic analogy. This proposal results in a versatile and functional inductorless implementation of the Chua`s circuit that offers new and interesting features for several applications. The analogous circuit is implemented and used to perform an experimental mapping of a large variety of attractors.