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/.

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.

Relation between sedimentary framework and hydrogeology in the Guarani Aquifer System in Sao Paulo state, Brazil

This paper presents the results of a new investigation of the Guarani Aquifer System (SAG) in Sao Paulo state. New data were acquired about sedimentary framework, flow pattern, and hydrogeochemistry. The flow direction in the north of the state is towards the southwest and not towards the west as expected previously. This is linked to the absence of SAG outcrop in the northeast of Sao Paulo state. Both the underlying Piramboia Formation and the overlying Botucatu Formation possess high porosity (18.9% and 19.5%, respectively), which was not modified significantly by diagenetic changes. Investigation of sediments confirmed a zone of chalcedony cement close to the SAG outcrop and a zone of calcite cement in the deep confined zone. The main events in the SAG post-sedimentary history were: (1) adhesion of ferrugineous coatings on grains, (2) infiltration of clays in eodiagenetic stage, (3) regeneration of coatings with formation of smectites, (4) authigenic overgrowth of quartz and K-feldspar in advanced eodiagenetic stage, (5) bitumen cementation of Piramboia Formation in mesodiagenetic stage, (6) cementation by calcite in mesodiagenetic and telodiagenetic stages in Piramboia Formation, (7) formation of secondary porosity by dissolution of unstable minerals after appearance of hydraulic gradient and penetration of the meteoric water caused by the uplift of the Serra do Mar coastal range in the Late Cretaceous, (8) authigenesis of kaolinite and amorphous silica in unconfined zone of the SAG and cation exchange coupled with the dissolution of calcite at the transition between unconfined and confined zone, and (9) authigenesis of analcime in the confined SAG zone. The last two processes are still under operation. The deep zone of the SAG comprises an alkaline pH, Na-HCO(3) groundwater type with old water and enriched delta(13)C values (<-3.9), which evolved from a neutral pH, Ca-HCO(3) groundwater type with young water and depleted delta(13)C values (>-18.8) close to the SAG outcrop. This is consistent with a conceptual geochemical model of the SAG, suggesting dissolution of calcite driven by cation exchange, which occurs at a relatively narrow front recently moving downgradient at much slower rate compared to groundwater flow. More depleted values of delta(18)O in the deep confined zone close to the Parana River compared to values of relative recent recharged water indicate recharge occur during a period of cold climate. The SAG is a ""storage-dominated"" type of aquifer which has to be managed properly to avoid its overexploitation. (C) 2011 Elsevier Ltd. All rights reserved.

Anticorrosive cerium-based coatings prepared by the sol-gel method

The development of efficient anti-corrosion and environmentally friendly coating systems are needed for the replacement of the highly toxic Cr-based conversion coatings for corrosion protection of aluminum alloys. In this study, we demonstrate that the direct application of ceramic cerium-based sol-gel coatings to AA7075-T6 substrates produces high-performance anti-corrosion layers. Electrochemical experiments and analyses of the microstructure demonstrate that the protective layers are very efficient for the passivation of the alloy surfaces operating as both passive and active barrier for corrosion protection.

Tribological Testing of Some Potential PVD and CVD Coatings for Steel Wire Drawing Dies

Cemented carbide is today the most frequently used drawing die material in steel wire drawing applications. This is mainly due to the possibility to obtain a broad combination of hardness and toughness thus meeting the requirements concerning strength, crack resistance and wear resistance set by the wire drawing process. However, the increasing cost of cemented carbide in combination with the possibility to increase the wear resistance of steel through the deposition of wear resistant CVD and PVD coatings have enhanced the interest to replace cemented carbide drawing dies with CVD and PVD coated steel wire drawing dies. In the present study, the possibility to replace cemented carbide wire drawing dies with CVD and PVD coated steel drawing dies have been investigated by tribological characterisation, i.e. pin-on-disc and scratch testing, in combination with post-test observations of the tribo surfaces using scanning electron microscopy, energy dispersive X-ray spectroscopy and 3D surface profilometry. Based on the results obtained, CVD and PVD coatings aimed to provide improved tribological performance of steel wire drawing dies should display a smooth surface topography, a high wear resistance, a high fracture toughness (i.e. a high cracking and chipping resistance) and intrinsic low friction properties in contact with the wire material. Also, the steel substrate used must display a sufficient load carrying capacity and resistance to thermal softening. Of the CVD and PVD coatings evaluated in the tribological tests, a CVD TiC and a PVD CrC/C coating displayed the most promising results.

Microstructural, Mechanical and Tribological Characterisation of CVD and PVD Coatings for Metal Cutting Applications

The present thesis focuses on characterisation of microstructure and the resulting mechanical and tribological properties of CVD and PVD coatings used in metal cutting applications. These thin and hard coatings are designed to improve the tribological performance of cutting tools which in metal cutting operations may result in improved cutting performance, lower energy consumption, lower production costs and lower impact on the environment.  In order to increase the understanding of the tribological behaviour of the coating systems a number of friction and wear tests have been performed and evaluated by post-test microscopy and surface analysis. Much of the work has focused on coating cohesive and adhesive strength, surface fatigue resistance, abrasive wear resistance and friction and wear behaviour under sliding contact and metal cutting conditions. The results show that the CVD deposition of accurate crystallographic phases, e.g. α-Al2O3 rather than κ-Al2O3, textures and multilayer structures can increase the wear resistance of Al2O3. However, the characteristics of the interfaces, e.g. topography as well as interfacial porosity, have a strong impact on coating adhesion and consequently on the resulting properties.  Through the deposition of well designed bonding and template layer structures the above problems may be eliminated. Also, the presence of macro-particles in PVD coatings may have a significant impact on the interfacial adhesive strength, increasing the tendency to coating spalling and lowering the surface fatigue resistance, as well as increasing the friction in sliding contacts. Finally, the CVD-Al2O3 coating topography influences the contact conditions in sliding as well as in metal cutting. In summary, the work illuminates the importance of understanding the relationships between deposition process parameters, composition and microstructure, resulting properties and tribological performance of CVD and PVD coatings and how this knowledge can be used to develop the coating materials of tomorrow.

A Gradient-Type Method For Real-Time State Estimation Of Water Distribution Networks

Drinking water distribution networks risk exposure to malicious or accidental contamination. Several levels of responses are conceivable. One of them consists to install a sensor network to monitor the system on real time. Once a contamination has been detected, this is also important to take appropriate counter-measures. In the SMaRT-OnlineWDN project, this relies on modeling to predict both hydraulics and water quality. An online model use makes identification of the contaminant source and simulation of the contaminated area possible. The objective of this paper is to present SMaRT-OnlineWDN experience and research results for hydraulic state estimation with sampling frequency of few minutes. A least squares problem with bound constraints is formulated to adjust demand class coefficient to best fit the observed values at a given time. The criterion is a Huber function to limit the influence of outliers. A Tikhonov regularization is introduced for consideration of prior information on the parameter vector. Then the Levenberg-Marquardt algorithm is applied that use derivative information for limiting the number of iterations. Confidence intervals for the state prediction are also given. The results are presented and discussed on real networks in France and Germany.