Basin of attraction of a cusp-fold singularity in 3D piecewise smooth vector fields

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Detecting changes in the basin of attraction of a dynamical system: Application to the postural restoring system

A method that provides athree-dimensional representation ofthe basin ofattraction of a dynamical system from experimen tal data was applied tothe problem ofdynamic balance restoration. The method isbased onthe density ofthe data onthe phase space ofthe system under study and makes use ofmodeling and numerical curve fittingtools.For the dynamical system ofbalance restora tion,the shape and the size of the basin of attraction depend on the dynamics of the postural restoring mechanisms and contain important information regarding the biomechanical,as well as the neuromuscular condition of the individual. The aim ofthis work was toexamine the ability ofthe method todetect, through the observed changes inthe shape and/or the size ofthe calculated basins of attraction, (a)the inherent differences between different systems (in the current application, postural restoring systems of different individuals)and (b)induced chan ges in the same system (thepostural restoring system of an individual).The results ofthe study confirm the validity of the method and furthermore justify its robustness.

Adaptive tackling of the swinging problem for a 2 DOF crane – payload system

The control of a crane carrying its payload by an elastic string corresponds to a task in which precise, indirect control of a subsystem dynamically coupled to a directly controllable subsystem is needed. This task is interesting since the coupled degree of freedom has little damping and it is apt to keep swinging accordingly. The traditional approaches apply the input shaping technology to assist the human operator responsible for the manipulation task. In the present paper a novel adaptive approach applying fixed point transformations based iterations having local basin of attraction is proposed to simultaneously tackle the problems originating from the imprecise dynamic model available for the system to be controlled and the swinging problem, too. The most important phenomenological properties of this approach are also discussed. The control considers the 4th time-derivative of the trajectory of the payload. The operation of the proposed control is illustrated via simulation results.

Periodic-orbit analysis and scaling laws of intermingled basins of attraction in an ecological dynamical system

Chaotic dynamical systems with two or more attractors lying on invariant subspaces may, provided certain mathematical conditions are fulfilled, exhibit intermingled basins of attraction: Each basin is riddled with holes belonging to basins of the other attractors. In order to investigate the occurrence of such phenomenon in dynamical systems of ecological interest (two-species competition with extinction) we have characterized quantitatively the intermingled basins using periodic-orbit theory and scaling laws. The latter results agree with a theoretical prediction from a stochastic model, and also with an exact result for the scaling exponent we derived for the specific class of models investigated. We discuss the consequences of the scaling laws in terms of the predictability of a final state (extinction of either species) in an ecological experiment.

Enlarging the domain of attraction of stable MPC controllers, maintaining the output performance

This work presents an alternative way to formulate the stable Model Predictive Control (MPC) optimization problem that allows the enlargement of the domain of attraction, while preserving the controller performance. Based on the dual MPC that uses the null local controller, it proposed the inclusion of an appropriate set of slacked terminal constraints into the control problem. As a result, the domain of attraction is unlimited for the stable modes of the system, and the largest possible for the non-stable modes. Although this controller does not achieve local optimality, simulations show that the input and output performances may be comparable to the ones obtained with the dual MPC that uses the LQR as a local controller. (C) 2009 Elsevier Ltd. All rights reserved.

Late Pliensbachian-Early Toarcian (Early Jurassic) environmental changes in an epicontinental basin of NW Europe (Causses area, central France): A micropaleontological and geochemical approach

We present an integrated work based on calcareous nannofossil and benthic foraminiferal assemblages, and geochemical analyses of two Upper Pliensbachian-Lower Toarcian sections located in the central-South France. The studied sections, Tournadous and Saint-Paul-des-Fonts, represent the proximal and the distal part, respectively, of the Jurassic Causses Basin, one of the small, partly enclosed basins belonging to the epicontinental shelf of the NW Tethys. At the transition from Late Pliensbachian to Early Toarcian, the Causses Basin recorded an emersion in response to the global sea-level fall. Our data indicate severe environmental conditions of marine waters, including salinity decrease and anoxia development, occurring in the Early Toarcian. The acme of this deterioration coincides with the Early Toarcian Anoxic Event (T-OAE) but, due to the restricted nature of the basin. anoxia persisted until the end of the Early Toarcian. mainly in the deeper parts of the basin. The micronutrients and organic organic-matter fluxes were probably high during the entire studied time interval, as shown by nannofossil and foraminiferal assemblages. However, nannoplankton production drastically decreased during the T-OAE, as demonstrated by very low nannofossil fluxes, and only taxa tolerant to low-saline surface waters could thrive. At the same time, benthic foraminifers temporarily disappeared in response to sea-bottom anoxia. Our study demonstrates that environmental changes related to the T-OAE are well-recorded even in small, partly enclosed basins of NW Europe, like the Causses Basin. Within this area, the effects of global changes. like sea sea-level and temperature fluctuations, are modulated by local conditions mainly controlled by the morphology of the basin. (C) 2008 Elsevier B.V. All rights reserved.

Local formation of varved sediments in a karstic collapse depression of Lake Banyoles (NE Spain)

Banyoles is the largest and deepest lake of karstic-tectonic origin in the Iberian Peninsula. The lake comprises several circular sub-basins characteri- zed by different oxygenation conditions at their hypolimnions. The multiproxy analysis of a > 5 m long sediment core combined with high resolution seis- mic stratigraphy (3.5 kHz pinger and multi-frequency Chirp surveys), allow a precise reconstruction of the evolution of a karstic depression (named B3) until present times. Local meromictic conditions in this sub-basin have been conducive to deposition and preservation of ca. 85 cm of varved sediments since the late 19th century. The onset of these conditions is likely related to lake waters eutrophication caused by increasing farming activities in the wa- tershed. Increasing clastic input and organic productivity during the second half of the 20th century have also been recorded within the laminated sedi- ments, revealing an intensification of human impact and warmer water tem- peratures.

STM probing of local oscillations of the Fano-Kondo effect: a Doniach-Sunjic approach for the Kondo peak

The use of the scanning tunneling microscope (STM) for the investigation of Kondo adatoms on normal metallic surfaces reveals a Fano-Kondo behavior of the conductance as a function of the tip bias. In this work, the Doniach-Sunjic expression is used to describe the Kondo peak and we analyze the effect of a complex Fano phase, arising from an external magnetic field, on the conductance pattern. It is demonstrated that such phase generates local oscillations of the Fano-Kondo line shape and can lead to the suppression of anti-resonances.

Stability region bifurcations of nonlinear autonomous dynamical systems: Type-zero saddle-node bifurcations

The behavior of stability regions of nonlinear autonomous dynamical systems subjected to parameter variation is studied in this paper. In particular, the behavior of stability regions and stability boundaries when the system undergoes a type-zero sadle-node bifurcation on the stability boundary is investigated in this paper. It is shown that the stability regions suffer drastic changes with parameter variation if type-zero saddle-node bifurcations occur on the stability boundary. A complete characterization of these changes in the neighborhood of a type-zero saddle-node bifurcation value is presented in this paper. Copyright (C) 2010 John Wiley & Sons, Ltd.

Spontaneous vegetation on overburden piles in the Coal Basin of Santa Catarina, Brazil

The objective of this work was to select indigenous vegetal species for restoration programs aiming at the regeneration of ombrophilous dense forest. Thirty-five spoil piles located in the county of Sideropolis, Santa Catarina, that received overburden disposal for 39 years (1950-1989) were selected for study because they exhibited remarkable spontaneous regrowth of trees compared to surrounding spoil piles. Floristic inventory covered the whole area of the 35 piles, whereas survey on phytosociology and natural regeneration studies were conducted in 70 plots distributed along the 35 piles. Floristic inventory recorded 83 species from 28 botanical families. Herbaceous terricolous plants constituted the predominant species (47.0%), followed by shrubs (26.5%), trees (19.3%), and vines (7.2%). Results from surveys on phytosociology and natural regeneration, focused on shrubs and trees, recorded incipient ecological succession. In addition, the most adapted species recorded on the overburden piles, as ranked by index of natural regeneration (RNT) plus importance value index (IVI), were as follows: Clethra scabra (RNT = 23.93%; IVI = 17.28%), Myrsine coriacea (RNT = 20.93%, IVI = 11.26%), Eupatorium intermedium (RNT 7.56%, IVI 0.40%), Miconia ligustroides (RNT 5.84%, IVI 2.37%), Ossaea amygdaloides (RNT 3.84%, IVI 1.30%), Tibouchina sellowiana (RNT 3.29%, M 1.94%), Eup. inulaefolium (RNT = 2.65%, IVI = 0.80%), and Baccharis dracunculifolia (RNT = 2.28%; IVI = 0.56%). High values of IVI and RNT exhibited by the exotic species Eucalyptus saligna (IVI = 21.73%, RNT = 51.41%) indicated strong competition between exotic and indigenous species. Severe chemical (acidic pH and lack of nutrients) and physical (coarse substrate and slope angle of 40-50 degrees) characteristics displayed by the overburden piles constituted limitations to floristic diversity and size of indigenous trees, indicating the need for substrate reclamation prior to forest restoration.

Stable MPC for tracking with maximal domain of attraction

In this work, a stable MPC that maximizes the domain of attraction of the closed-loop system is proposed. The proposed approach is suitable to real applications in the sense that it accounts for the case of output tracking, it is offset free if the output target is reachable and minimizes the offset if some of the constraints are active at steady state. The new approach is based on the definition of a Minkowski functional related to the input and terminal constraints of the stable infinite horizon MPC. It is also shown that the domain of attraction is defined by the system model and the constraints, and it does not depend on the controller tuning parameters. The proposed controller is illustrated with small order examples of the control literature. (C) 2011 Elsevier Ltd. All rights reserved.

A strategy to fill gaps in soil survey over large spatial extents: an example from the Murray-Darling basin of Australia

We re-mapped the soils of the Murray-Darling Basin (MDB) in 1995-1998 with a minimum of new fieldwork, making the most out of existing data. We collated existing digital soil maps and used inductive spatial modelling to predict soil types from those maps combined with environmental predictor variables. Lithology, Landsat Multi Spectral Scanner (Landsat MSS), the 9-s digital elevation model (DEM) of Australia and derived terrain attributes, all gridded to 250-m pixels, were the predictor variables. Because the basin-wide datasets were very large data mining software was used for modelling. Rule induction by data mining was also used to define the spatial domain of extrapolation for the extension of soil-landscape models from existing soil maps. Procedures to estimate the uncertainty associated with the predictions and quality of information for the new soil-landforms map of the MDB are described. (C) 2002 Elsevier Science B.V. All rights reserved.

Local delivery of EGF-liposome mediated bone modeling in orthodontic tooth movement by increasing RANKL expression

Aims: It has long been demonstrated that epidermal growth factor (EGF) has catabolic effects oil bone. Thus. we examined the role of EGF in regulating mechanically induced bone modeling in a rat model of orthodontic tooth movement. Main methods: The maxillary first molars of rats were moved mesially using an orthodontic appliance attached to the maxillary incisor teeth. Rats were randomly divided into 4 groups: (G1) administration of PBS (Phosphate buffer saline Solution (n = 24); (G2) administration of empty liposomes (it = 24): (Q) administration 20 rig of EGF Solution (n = 24): and (G4) 20 ng of EGF-liposomes Solution (it = 24). Each Solution was injected in the mucosa of the left first molar adjacent to the appliance. At days 5, 10, 14 and 2 1 after drug administration. 6 animals of each group were sacrificed. Histomorphometric analysis was used to quantify osteoclasts (Tartrate-resistant acid phosphatase (TRAP) + cells) and tooth movement. Using immunohistochemistry assay we evaluated the RANKL (receptor activator of nuclear factor kappa B ligand) and epidermal growth factor receptor (EGFR) expression. Key findings: The EGF-liposome administration showed an increased tooth movement and osteoclast numbers compared to controls (p<0.05). This was correlated with intense RANKL expression. Both osteoblasts and osteoclasts expressed EGFR. Significance: Local delivery of EGF-liposome stimulates, osteoclastogenesis and tooth movement. (C) 2009 Elsevier Inc. All rights reserved.

Local dispersion of the Eucalyptus leaf beetle Chrysophtharta bimaculata (Coleoptera: Chrysomelidae), and implications for forest protection

1. Chrysophtharta bimaculata is a native chrysomelid species that can cause chronic defoliation of plantation and regrowth Eucalyptus forests in Tasmania, Australia. Knowledge of the dispersion pattern of C. bimaculata was needed in order to assess the efficiency of an integrated pest management (IPM) programme currently used for its control. 2. Using data from yellow flight traps, local populations of C. bimaculata adults were monitored over a season at spatial scales relevant to commercial forestry: within a 50-ha operational management unit (a forestry 'coupe') and between coupes. In addition, oviposition was monitored over a season at a subset of the between-coupe sites. 3. Dispersion indices (Taylor's Power Law and Iwao's Mean Crowding regression method) demonstrated that C. bimaculata adults were spatially aggregated within and between coupes, although the number of egg-batches laid at the between-coupe scale was uniform. Spatial autocorrelation analysis showed that trap-catches at the within-coupe level were similar (positively autocorrelated) to a radius distance of approximately 110 m, and then dissimilar (negatively autocorrelated) at approximately 250 m. At the between-coupe scale, no repeatable spatial autocorrelation patterns were observed. 4. For any individual site, rapid changes in beetle density were observed to be associated with loosely aggregated flights of beetles into and out of that site. Peak adult catches (> the weekly mean plus standard deviation trap-catch) for a site occurred for a period of 2.0 +/- 0.22 weeks at a time (n = 37), with normally only one or two peaks per site per season. Peak oviposition events for a site occurred on average 1.4 +/- 0.11 times per season and lasted 1.5 +/- 0.12 weeks. 5. Analysis of an extensive data set (n = 417) demonstrated that adult abundance at a site was positively correlated with egg density, but negatively correlated with tree damage (caused by conspecifics) and the presence of conspecific larvae. There was no relationship between adult abundance and a visual estimate of the amount of young foliage on trees. 6. Adults of C. bimaculata are show n to occur in relatively small, mobile aggregations. This means that pest surveys must be both regular (less than 2 weeks apart) and intensive (with sampling points no more than 150 m apart) if beetle populations are to be monitored with confidence. Further refinement of the current IPM strategy must recognize the problems posed by this temporal and spatial patchiness, particularly with regard to the use of biological insecticides, such as Bacillus thuringiensis, for which only a very short operational window exists.