Dynamics in dumbbell domains II. The limiting problem

In this work we continue the analysis of the asymptotic dynamics of reaction-diffusion problems in a dumbbell domain 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 (2) (2006) 551-597]. Here we study the limiting problem, that is, an evolution problem in a ""domain"" which consists of an open, bounded and smooth set Omega subset of R(N) with a curve R(0) attached to it. The evolution in both parts of the domain is governed by a parabolic equation. In Omega the evolution is independent of the evolution in R(0) whereas in R(0) the evolution depends on the evolution in Omega through the continuity condition of the solution at the junction points. We analyze in detail the linear elliptic and parabolic problem, the generation of linear and nonlinear semigroups, the existence and structure of attractors. (C) 2009 Elsevier Inc. All rights reserved.

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.

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.

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.

A etnoarqueologia na Amazônia: contribuições e perspectivas

Desde a década de 1970, a etnoarqueologia tem sido realizada na região amazônica com diferentes temas, problemas e objetivos. Independentemente das suas perspectivas, esses trabalhos têm contribuído para o entendimento da pré-história amazônica, ampliando as possibilidades para interpretar o registro arqueológico. Além disso, contribuem na crítica e na revisão dos paradigmas tradicionais que dominaram por muito tempo as explicações sobre os modos de vida das populações amazônicas do presente e do passado. Esse artigo apresenta um panorama desses trabalhos etnoarqueológicos, salientando sua importância para o entendimento da pré-história amazônica e para a continuidade das pesquisas arqueológicas na região.

Deep weathering and landscape evolution in a tropical plateau

The thick weathering profiles of humid tropical areas are an important, yet generally neglected, source of information on landscape evolution. Six complete profiles of the weathering mantle were sampled by drilling on the three stepped levels of the Campos do Jordao Plateau, on the NW flank of the Continental Rift of Southeastern Brazil. Mineralogical and micromorphological analyses of drill core samples, complemented by geochemical interpretations and by previous data on the upper saprolite, indicate continuity of a general lateritic trend during the entire process of mantle formation. Lateritization phases of different intensity were defined and considered to reflect adjustment to changes in environmental conditions created by the gradual uplift of the plateau to its present position. Older and more superficial materials related to intense lateritic weathering are characterized by allitization with direct formation of gibbsite from silicates, probably related to tropical climates existing immediately before the formation of the continental rift, during the Paleogene, and also before any significant increase in altitude. Monosialitization phase with general kaolinitization and restricted indirect formation of gibbsite from silicates could be associated to less aggressive climates that followed the Neogene (Miocene?) accentuation of uplift rates along the continental rift. The changes produced by uplift in the tropical climate eventually favored the development of a podzolization trend in soils above 1800m. (C) 2011 Elsevier BM. All rights reserved.

Shelter association between the hermit crab Sympagurus dimorphus and the zoanthid Epizoanthus paguricola in the southwestern Atlantic Ocean

Schejter, L. and Mantelatto, F.L. 2011. Shelter association between the hermit crab Sympagurus dimorphus and the zoanthid Epizoanthus paguricola in the southwestern Atlantic Ocean. -Acta Zoologica (Stockholm) 92: 141-149. The available literature on zoanthid-hermit crab associations deals only with records of this phenomenon, providing no detailed information. We describe, for the first time, the shell-like colonies of Epizoanthus paguricola associated with the hermit crab Sympagurus dimorphus from benthic samples taken in the Argentine Sea, between 85 and 131 m depth, and provide information about morphometric relationships between the hermits and the zoanthids. In total, 260 specimens (137 males and 123 females) of S. dimorphus were collected, 240 (92.3%) of which were living in symbiosis with E. paguricola. The remaining 20 (7.7%) were living inside gastropod shells. As the initial structure of the pseudoshell, 12 different gastropod species were found (all were almost totally covered with colonies of E. paguricola). The hermit crab lives in the spiral cavity inside the soft colony, which seemed to be slightly different depending on the initial gastropod. Aperture pseudoshell morphology did not seem to be related to the sex of the hermit crab host, although males showed larger apertures for a given colony size. This fact is probably related to a larger size of male`s cheliped (sexual dimorphic character) used like a gastropod operculum and that may serve as a template for the growing of the aperture pseudoshell edge. The number of epizoanthid polyps per colony increased in relation to the weight of the colony and to the size of the hermit crab. A process of selection of the initial shell was evident, because species of Naticidae were not the most common gastropods in this benthic community, but were those most used by hermit crabs (> 60%). The puzzling association between hermit crab, shell and zoanthid presumably occurs during the hermit juvenile phase, when the crab occupies a small shell, and a zoanthid larva settles on it. Given the close relationship between S. dimorphus and E. paguricola found in this region, we support the idea that due to the low availability of adequate gastropod shells for hermit life cycle, this association allows the establishment and the continuity of the hermit crab population in the studied area.

History teaching today: wanderings, gains and losses

This article analyzes traditions of debate about the teaching of history in Brazil since the 1964-1984 dictatorship. It discusses the changes, continuities, achievements and losses in the history of the discipline. It emphasizes the importance of school culture, the necessary continuity of the school as an institution and dialogue with non-school forms of education.

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.

Existence of pullback attractors for pullback asymptotically compact processes

This paper is concerned with the existence of pullback attractors for evolution processes. Our aim is to provide results that extend the following results for autonomous evolution processes (semigroups) (i) An autonomous evolution process which is bounded, dissipative and asymptotically compact has a global attractor. (ii) An autonomous evolution process which is bounded, point dissipative and asymptotically compact has a global attractor. The extension of such results requires the introduction of new concepts and brings up some important differences between the asymptotic properties of autonomous and non-autonomous evolution processes. An application to damped wave problem with non-autonomous damping is considered. (C) 2009 Elsevier Ltd. All rights reserved.

An extension of the concept of gradient semigroups which is stable under perturbation

In this article we introduce the concept of a gradient-like nonlinear semigroup as an intermediate concept between a gradient nonlinear semigroup (those possessing a Lyapunov function, see [J.K. Hale, Asymptotic Behavior of Dissipative Systems, Math. Surveys Monogr., vol. 25, Amer. Math. Soc., 1989]) and a nonlinear semigroup possessing a gradient-like attractor. We prove that a perturbation of a gradient-like nonlinear semigroup remains a gradient-like nonlinear semigroup. Moreover, for non-autonomous dynamical systems we introduce the concept of a gradient-like evolution process and prove that a non-autonomous perturbation of a gradient-like nonlinear semigroup is a gradient-like evolution process. For gradient-like nonlinear semigroups and evolution processes, we prove continuity, characterization and (pullback and forwards) exponential attraction of their attractors under perturbation extending the results of [A.N. Carvalho, J.A. Langa, J.C. Robinson, A. Suarez, Characterization of non-autonomous attractors of a perturbed gradient system, J. Differential Equations 236 (2007) 570-603] on characterization and of [A.V. Babin, M.I. Vishik, Attractors in Evolutionary Equations, Stud. Math. Appl.. vol. 25, North-Holland, Amsterdam, 1992] on exponential attraction. (C) 2009 Elsevier Inc. All rights reserved.

Morpho-Anatomical Analysis of the Rhizome in Species of Scleria Berg. (Cyperaceae) from Serra do Cipó (MG)

Aspects related to the nature of stem thickening in monocotyledons have been the subject of many studies. Primary thickening has been attributed to the Primary Thickening Meristem (PTM). According to most authors, it gives rise, besides the adventitious roots, to the vascular tissues and part of the cortex. In other words, it has centripetal and centrifugal activity. For some authors, however, it gives rise only to the vascular system, and for others, only to part of the cortex. However, this work demonstrated that PTM corresponds to the pericycle in the meristematic phase or to the pericycle associated with the endodermis, also with meristematic activity. It was observed that the pericycle was responsible for the formation of the vascular system of the rhizome and of the adventitious roots; the endodermis gave rise to cell layers with radial disposition which comprised the inner portion of the stem cortex, and which corresponded to the region known as the derivatives of the meristematic endodermis (DME). A continuity was also demonstrated between the tissues of the stem and root in species of Scleria Berg. (Cyperaceae).

The viscosity parameter's dependence on the profile of the disk scale height

It is shown that, for accretion disks, the height scale is a constant whenever hydrostatic equilibrium and the subsonic turbulence regime hold in the disk. In order to have a variable height scale, processes are needed that contribute an extra term to the continuity equation. This contribution makes the viscosity parameter much greater in the outer region and much smaller in the inner region. Under these circumstances, turbulence is the presumable source of viscosity in the disk.

LOCAL WELL POSEDNESS, ASYMPTOTIC BEHAVIOR AND ASYMPTOTIC BOOTSTRAPPING FOR A CLASS OF SEMILINEAR EVOLUTION EQUATIONS OF THE SECOND ORDER IN TIME

A class of semilinear evolution equations of the second order in time of the form u(tt)+Au+mu Au(t)+Au(tt) = f(u) is considered, where -A is the Dirichlet Laplacian, 92 is a smooth bounded domain in R(N) and f is an element of C(1) (R, R). A local well posedness result is proved in the Banach spaces W(0)(1,p)(Omega)xW(0)(1,P)(Omega) when f satisfies appropriate critical growth conditions. In the Hilbert setting, if f satisfies all additional dissipativeness condition, the nonlinear Semigroup of global solutions is shown to possess a gradient-like attractor. Existence and regularity of the global attractor are also investigated following the unified semigroup approach, bootstrapping and the interpolation-extrapolation techniques.

Dynamical estimates of chaotic systems from Poincare recurrences

We show a function that fits well the probability density of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space. It deviates from the exponential statistics by a small power-law term, a term that represents the deterministic manifestation of the dynamics. We also show how one can quickly and easily estimate the Kolmogorov-Sinai entropy and the short-term correlation function by realizing observations of high probable returns. Our analyses are performed numerically in the Henon map and experimentally in a Chua's circuit. Finally, we discuss how our approach can be used to treat the data coming from experimental complex systems and for technological applications. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3263943]