Estimating Attractor Dimension on the Nonlinear Pendulum Time Series

Chaotic dynamical systems exhibit trajectories in their phase space that converges to a strange attractor. The strangeness of the chaotic attractor is associated with its dimension in which instance it is described by a noninteger dimension. This contribution presents an overview of the main definitions of dimension discussing their evaluation from time series employing the correlation and the generalized dimension. The investigation is applied to the nonlinear pendulum where signals are generated by numerical integration of the mathematical model, selecting a single variable of the system as a time series. In order to simulate experimental data sets, a random noise is introduced in the time series. State space reconstruction and the determination of attractor dimensions are carried out regarding periodic and chaotic signals. Results obtained from time series analyses are compared with a reference value obtained from the analysis of mathematical model, estimating noise sensitivity. This procedure allows one to identify the best techniques to be applied in the analysis of experimental data.

An Investigation into Mechanisms of Loss of Safe Basins in a 2 D.O.F. Nonlinear Oscillator

In this work we consider the transient stability of coupled motions of a 2 D.O.F. nonlinear oscillator that can represent, for example, the motions of a sea vessel under the action of trains of regular lateral waves. Instability is studied as the escape of the system from a safe potential well. The set of initial conditions in phase space that lead to acceptable motions constitutes its safe basin. We investigate the evolution of these safe basins under variation of parameters such as frequency and amplitude of waves, and an internal tuning parameter. Complex nonlinear phenomena are known to play an important role in determining the loss of safe basins as, say, wave amplitude is increased. We therefore investigate those processes, and attempt to classify them in terms of their speed relative to changes in parameter values. "Mechanism basins" are produced depicting regions of parameter space in which rapid or slow losses of safe basin are observed. We propose that a comprehensive understanding of mechanisms of loss of safe basins can be a valuable tool in assessing stability properties of these systems, and we give a conceptual view of how such information could be used.

Head Space Solid Phase Micro-Extraction (HS - SPME) of volatile organic compounds produced by Sporidiobolus salmonicolor (CBS 2636)

The aim of the present study was the assessment of volatile organic compounds produced by Sporidiobolus salmonicolor (CBS 2636) using methyl and ethyl ricinoleate, ricinoleic acid and castor oil as precursors. The analysis of the volatile organic compounds was carried out using Head Space Solid Phase Micro-Extraction (HS - SPME). Factorial experimental design was used for investigating extraction conditions, verifying stirring rate (0-400 rpm), temperature (25-60 ºC), extraction time (10-30 minutes), and sample volume (2-3 mL). The identification of volatile organic compounds was carried out by Gas Chromatography with Mass Spectrum Detector (GC/MSD). The conditions that resulted in maximum extraction were: 60 ºC, 10 minutes extraction, no stirring, sample volume of 2.0 mL, and addition of saturated KCl (1:10 v/v). In the bio-production of volatile organic compounds the effect of stirring rate (120-200 rpm), temperature (23-33 ºC), pH (4.0-8.0), precursor concentration (0.02-0.1%), mannitol (0-6%), and asparagine concentration (0-0.2%) was investigated. The bio-production at 28 ºC, 160 rpm, pH 6,0 and with the addition of 0.02% ricinoleic acid to the medium yielded the highest production of VOCs, identified as 1,4-butanediol, 1,2,2-trimethylciclopropilamine, beta-ionone; 2,3-butanodione, pentanal, tetradecane, 2-isononenal, 4-octen-3-one, propanoic acid, and octadecane.

Eosinophil levels in the acute phase of experimental chagas' disease

Eosinophil dynamics, in bone marrow, blood and peritoneal exudate, of resistant C57B1/6 (C57) and susceptible A/Snell (A/Sn) mice was comparatively studied during the acute phase of infection by Trypanosoma cruzi Y strain. A decline was observed in bone marrow eosinophil levels in A/Sn, but not in C57 mice, soon after infection, those of the former remaining significantly below those of the latter up to the 4th day of infection. Bone marrow eosinophil levels of C57 mice declined subsequently to levels comparable to those of A/Sn mice, the number of these cells in this compartment remaining 50% those of non infected controls, in both strains, up to the end of the experiment on the 14th day of infection. The fluctuations in eosinophil levels in blood and peritoneal space were similar in both mice strains studied. Concomitantly with depletion of eosinophils in the marrow, depletion in blood and a marked rise of these cells in the peritoneal space, initial site of infection, occurred in both strains. The difference in eosinophil bone marrow levels, between C57 and A/Sn mice, observed in the first four days of infection, suggests a higher eosinopoiesis capacity of the former in this period, which might contribute to their higher resistance to T. cruzi infection.

Calomys callosus: an alternative model to study fibrosis in Schistosomiasis mansoni: the pathology of the acute phase

Twenty Calomys callosus, Rengger, 1830 (Rodentia-Cricetidae) were studied in the early stage of the acute schistosomal mansoni infection (42nd day). The same number of Swiss Webster mice were used as a comparative standard. Liver and intestinal sections, fixed in formalin-Millonig and embedded in paraffin, were stained with hematoxilin and eosin, PAS-Alcian Blue, pH = 1.0 and 2.5, Lennert's Giemsa, Picrosirius plus polarization microscopy, Periodic acid methanamine silver, Gomori's silver reticulin and resorcin-fuchsin. Immunohistological study (indirect immunofluorescence and peroxidase labeled extravidin-biotin methods) was done with antibodies specific to pro-collagen III, fibronectin, elastin, condroitin-sulfate, tenascin, alpha smooth muscle actin, vimentin and desmin. The hepatic granulomas were small, reaching only 27 of the volume of the hepatic Swiss Webster granuloma. They were composed mainly by large immature macrophages, often filled by schistosomal pigment, characterizing an exsudative-macrophage granuloma type. The granulomas were situated in the parenchyma and in the portal space. They were often intravascular, poor of extracellular matrix components, except fibronectin and presented, sometimes alpha smooth muscle actin and vimentin positive cells. The C. callosus intestinal granulomas were similar to Swiss Webster, showing predominance of macrophages. Therefore, the C. callosus acquire very well the Schistosoma mansoni infection, without developing strong hepatic acute granulomatous reaction, suggesting lack of histopathological signs of hypersensitivity.