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.

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.

Stability of gradient semigroups under perturbations

In this paper we prove that gradient-like semigroups (in the sense of Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) are gradient semigroups (possess a Lyapunov function). This is primarily done to provide conditions under which gradient semigroups, in a general metric space, are stable under perturbation exploiting the known fact (see Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) that gradient-like semigroups are stable under perturbation. The results presented here were motivated by the work carried out in Conley (1978 Isolated Invariant Sets and the Morse Index (CBMS Regional Conference Series in Mathematics vol 38) (RI: American Mathematical Society Providence)) for groups in compact metric spaces (see also Rybakowski (1987 The Homotopy Index and Partial Differential Equations (Universitext) (Berlin: Springer)) for the Morse decomposition of an invariant set for a semigroup on a compact metric space).

Reduced gradient method combined with augmented Lagrangian and barrier for the optimal power flow problem

A new approach for solving the optimal power flow (OPF) problem is established by combining the reduced gradient method and the augmented Lagrangian method with barriers and exploring specific characteristics of the relations between the variables of the OPF problem. Computer simulations on IEEE 14-bus and IEEE 30-bus test systems illustrate the method. (c) 2007 Elsevier Inc. All rights reserved.

Partial spectral projected gradient method with active-set strategy for linearly constrained optimization

A method for linearly constrained optimization which modifies and generalizes recent box-constraint optimization algorithms is introduced. The new algorithm is based on a relaxed form of Spectral Projected Gradient iterations. Intercalated with these projected steps, internal iterations restricted to faces of the polytope are performed, which enhance the efficiency of the algorithm. Convergence proofs are given and numerical experiments are included and commented. Software supporting this paper is available through the Tango Project web page: http://www.ime.usp.br/similar to egbirgin/tango/.

Hypotheses testing for structural calibration model

The main objective of this paper is to discuss maximum likelihood inference for the comparative structural calibration model (Barnett, in Biometrics 25:129-142, 1969), which is frequently used in the problem of assessing the relative calibrations and relative accuracies of a set of p instruments, each designed to measure the same characteristic on a common group of n experimental units. We consider asymptotic tests to answer the outlined questions. The methodology is applied to a real data set and a small simulation study is presented.

Patterns of water and heat flux across a biome gradient from tropical forest to savanna in Brazil

We investigated the seasonal patterns of water vapor and sensible heat flux along a tropical biome gradient from forest to savanna. We analyzed data from a network of flux towers in Brazil that were operated within the Large-Scale Biosphere-Atmosphere Experiment in Amazonia (LBA). These tower sites included tropical humid and semideciduous forest, transitional forest, floodplain (with physiognomies of cerrado), and cerrado sensu stricto. The mean annual sensible heat flux at all sites ranged from 20 to 38 Wm(-2), and was generally reduced in the wet season and increased in the late dry season, coincident with seasonal variations of net radiation and soil moisture. The sites were easily divisible into two functional groups based on the seasonality of evaporation: tropical forest and savanna. At sites with an annual precipitation above 1900 mm and a dry season length less than 4 months (Manaus, Santarem and Rondonia), evaporation rates increased in the dry season, coincident with increased radiation. Evaporation rates were as high as 4.0 mm d(-1) in these evergreen or semidecidous forests. In contrast, ecosystems with precipitation less than 1700 mm and a longer dry season (Mato Grosso, Tocantins and Sao Paulo) showed clear evidence of reduced evaporation in the dry season. Evaporation rates were as low as 2.5 mm d(-1) in the transitional forests and 1 mm d(-1) in the cerrado. The controls on evapotranspiration seasonality changed along the biome gradient, with evaporative demand (especially net radiation) playing a more important role in the wetter forests, and soil moisture playing a more important role in the drier savannah sites.

Role of Surfactants in Carbon Nanotubes Density Gradient Separation

Several strategies aimed at sorting single-walled carbon nanotubes (SWNT) by diameter and/or electronic structure have been developed in recent years. A nondestructive sorting method was recently proposed in which nanotube bundles are dispersed in water-surfactant solutions and submitted to ultracentrifugation in a density gradient. By this method, SWNTs of different diameters are distributed according to their densities along the centrifuge tube. A mixture of two anionic amphiphiles, namely sodium dodecylsulfate (SIDS) and sodium cholate (SC), presented the best performance in discriminating nanotubes by diameter. We present molecular dynamics studies of the water-surfactant-SWNT system. The simulations revealed one aspect of the discriminating power of surfactants: they can actually be attracted toward the interior of the nanotube cage. The binding energies of SDS and SC on the outer nanotube surface are very similar and depend weakly on diameter. The binding inside the tubes, on the contrary, is strongly diameter dependent: SDS fits best inside tubes with diameters ranging from 8 to 9 angstrom, while SC is best accommodated in larger tubes, with diameters in the range 10.5-12 angstrom. The dynamics at room temperature showed that, as the amphiphile moves to the hollow cage, water molecules are dragged together, thereby promoting the nanotube filling. The resulting densities of filled SWNT are in agreement with measured densities.

Chemostratigraphy of the Tamengo Formation (Corumba Group, Brazil) A contribution to the calibration of the Ediacaran carbon-isotope curve

The Corumba Group cropping out in the southern Paraguay Belt in Brazil is one of the most complete Ediacaran sedimentary archives of palaeogeographic climatic biogeochemical and biotic evolution in southwestern Gondwana The unit hosts a rich fossil record including acritarchs vendotaenids (Vendo taenia Eoholynia) soft-bodied metazoans (Corumbella) and skeletal fossils (Cloudina Titanotheca) The Tamengo Formation made up mainly of limestones and marls provides a rich bio- and chemostratigraphic record Several outcrops formerly assigned to the Cuiaba Group are here included in the Tamengo Formation on the basis of lithological and chemostratigraphical criteria High-resolution carbon isotopic analyses are reported for the Tamengo Formation showing (from base to top) (1) a positive delta(13)C excursion to +4 parts per thousand PDB above post-glacial negative values (2) a negative excursion to -3 5 parts per thousand associated with a marked regression and subsequent transgression (3) a positive excursion to +5 5 parts per thousand and (4) a plateau characterized by delta(13)C around +3 parts per thousand A U-Pb SHRIMP zircon age of an ash bed Interbedded in the upper part of the delta(13)C positive plateau yielded 543 +/- 3 Ma which is considered as the depositional age (Babinski et al 2008a) The positive plateau in the upper Tamengo Formation and the preceding positive excursion are ubiquitous features in several successions worldwide including the Nama Group (Namibia) the Dengying Formation (South China) and the Nafun and Ara groups (Oman) This plateau is constrained between 542 and 551 Ma thus consistent with the age of the upper Tamengo Formation The negative excursion of the lower Tamengo Formation may be correlated to the Shuram-Wonoka negative anomaly although delta(13)C values do not fall beyond -3 5 parts per thousand in the Brazilian sections Sedimentary breccias occur just beneath this negative excursion in the lower Tamengo Formation One possible interpretation of the origin of these breccias is a glacioeustatic sea-level fall but a tectonic interpretation cannot be completely ruled out Published by Elsevier B V

Metamorphic P-T evolution of granulites in the central Ribeira Fold Belt, SE Brazil

Pseudosections, geothermobarometric estimates and careful petrographic observations of gneissic migmatites and granulites from Neoproterozoic central Ribeira Fold Belt (SE Brazil) were performed in order to quantify the metamorphic P-T conditions during prograde and retrograde evolution of the Brasiliano Orogeny. Results establish a prograde metamorphic trajectory from amphibolite facies conditions to metamorphic peak (T = 850 +/- 50 A degrees C; P = 8 +/- 1 kbar) that promoted widespread dehydrationmelting of 30 to 40% of the gneisses and high-grade granitization. After the metamorphic peak, migmatites evolved with cooling and decompression to T a parts per thousand 500 A degrees C and P a parts per thousand 5 kbar coupled with aH2O increase, replacing the high-grade paragenesis plagioclase-quartz-K-feldspar-garnet by quartz-biotite-sillimanite-(muscovite). Cordierite absence, microtextural observations and P-T results constrain the migmatite metamorphic evolution in the pseudosections as a clockwise P-T path with retrograde cooling and decompression. High-temperature conditions further dehydrated the lower crust with biotite and amphibole-dehydration melting and granulite formation coupled with 10% melt generation. Granulites can thus be envisaged as middle to lower crust dehydrated restites. Granulites were slowly (nearly isobarically) cooled, followed by late exhumation/retrograde rapid decompression and cooling, reflecting a two step P-T path. This retrograde evolution, coupled with water influx, chemically reequilibrated the rocks from granulite to amphibolite/greenschist facies, promoting the replacement of the plagioclase-quartz-garnet-hypersthene peak assemblage by quartz-biotite- K-feldspar symplectites.

Holocene fires in East Amazonia (Caraja`s), new evidences, chronology and relation with paleoclimate

Past studies have evidenced the presence of charcoal in soils and lacustrine sediments of Amazonia region and suggested occurrences of widespread fires during the Middle Holocene. However, the available records do not indicate the changes in fire regime with enough time resolution. We quantified charcoal fragments in lacustrine sediments in a lake of North Carajas plateau in East Amazonia (5 degrees 50`-6 degrees 35`S and 49 degrees 30`-52 degrees 00`W). The charcoal quantification was compared to other sediment proxies, allowing a connection between paleofires and climate changes. Large variations in sediment characteristics led to distinct stages of sedimentation. From 11,800 (base of CSN 93/4) to 4750 cal yr B.P., low accumulation rates of organic matter are observed. Between 7600 cal yr B.P. (base of CSN 93/3 core) and 4750 cal yr B.P., this initial phase of sedimentation is characterized by low chlorophyll derivate accumulation rates and high accumulation rates of Botryococcus braunii, an alga resistant to episodic drought. The first phase of sedimentation would therefore correspond to, a low take level and a drier climate than today. Large biomass burning events occurred between 7450 cal yr B.P. and 4750 cal yr B.P., as indicated by the high charcoal particle concentration. From 4750 cal yr B.P. to 2800 cal yr B.P., accumulation rates of charcoal particles decreased, and the accumulation rate of chlorophyll derivate was low. From 2800 cal yr B.P. to 1300 cal yr B.P., the charcoal accumulation rates reached their lowest values in the core and a rapid increase in lacustrine production is evidenced by the increase in chlorophyll derivates and carbon accumulation rate. From 1300 cal yr B.P. to the last century, the charcoal accumulation rates increased. During the most recent period, the record is characterized by high accumulation rates of chlorophyll derivates while the charcoal particle accumulation rate decreased. This region is still unaffected by the current increase of anthropogenic fires. (c) 2007 Elsevier B.V. All rights reserved.

Heteroscedastic controlled calibration model applied to analytical chemistry

In chemical analyses performed by laboratories, one faces the problem of determining the concentration of a chemical element in a sample. In practice, one deals with the problem using the so-called linear calibration model, which considers that the errors associated with the independent variables are negligible compared with the former variable. In this work, a new linear calibration model is proposed assuming that the independent variables are subject to heteroscedastic measurement errors. A simulation study is carried out in order to verify some properties of the estimators derived for the new model and it is also considered the usual calibration model to compare it with the new approach. Three applications are considered to verify the performance of the new approach. Copyright (C) 2010 John Wiley & Sons, Ltd.

A Bayesian Semiparametric Approach for Solving the Discrete Calibration Problem

In this article, we introduce a semi-parametric Bayesian approach based on Dirichlet process priors for the discrete calibration problem in binomial regression models. An interesting topic is the dosimetry problem related to the dose-response model. A hierarchical formulation is provided so that a Markov chain Monte Carlo approach is developed. The methodology is applied to simulated and real data.

On the skew-normal calibration model

In this article, we present the EM-algorithm for performing maximum likelihood estimation of an asymmetric linear calibration model with the assumption of skew-normally distributed error. A simulation study is conducted for evaluating the performance of the calibration estimator with interpolation and extrapolation situations. As one application in a real data set, we fitted the model studied in a dimensional measurement method used for calculating the testicular volume through a caliper and its calibration by using ultrasonography as the standard method. By applying this methodology, we do not need to transform the variables to have symmetrical errors. Another interesting aspect of the approach is that the developed transformation to make the information matrix nonsingular, when the skewness parameter is near zero, leaves the parameter of interest unchanged. Model fitting is implemented and the best choice between the usual calibration model and the model proposed in this article was evaluated by developing the Akaike information criterion, Schwarz`s Bayesian information criterion and Hannan-Quinn criterion.

Skew-normal linear calibration: a Bayesian perspective

In this paper, we present a Bayesian approach for estimation in the skew-normal calibration model, as well as the conditional posterior distributions which are useful for implementing the Gibbs sampler. Data transformation is thus avoided by using the methodology proposed. Model fitting is implemented by proposing the asymmetric deviance information criterion, ADIC, a modification of the ordinary DIC. We also report an application of the model studied by using a real data set, related to the relationship between the resistance and the elasticity of a sample of concrete beams. Copyright (C) 2008 John Wiley & Sons, Ltd.