Numerical bifurcation analysis of two coupled FitzHugh-Nagumo oscillators

The behavior of neurons can be modeled by the FitzHugh-Nagumo oscillator model, consisting of two nonlinear differential equations, which simulates the behavior of nerve impulse conduction through the neuronal membrane. In this work, we numerically study the dynamical behavior of two coupled FitzHugh-Nagumo oscillators. We consider unidirectional and bidirectional couplings, for which Lyapunov and isoperiodic diagrams were constructed calculating the Lyapunov exponents and the number of the local maxima of a variable in one period interval of the time-series, respectively. By numerical continuation method the bifurcation curves are also obtained for both couplings. The dynamics of the networks here investigated are presented in terms of the variation between the coupling strength of the oscillators and other parameters of the system. For the network of two oscillators unidirectionally coupled, the results show the existence of Arnold tongues, self-organized sequentially in a branch of a Stern-Brocot tree and by the bifurcation curves it became evident the connection between these Arnold tongues with other periodic structures in Lyapunov diagrams. That system also presents multistability shown in the planes of the basin of attractions.     

Application of Fluorescence to the Study of Crude Petroleum

Crude petroleum oils are complex mixtures of different compounds (mainly organic), which are obtained from an extensive range of different geological sources. The fluorescence of crude petroleum oils derives largely from the aromatic hydrocarbon fraction, and this fluorescence emission is strongly influenced by the chemical composition (e.g., fluorophore and quencher concentrations) and physical characteristics (e.g., viscosity and optical density) of the oil. The fluorescence spectroscopy (FS) is increasingly used in petroleum technology due the availability of better optical detection techniques, because FS offers high sensitivity, good diagnostic potential, and relatively simple instrumentation. In this work we analyzed crude petroleum at different dilution in Nujol, a transparent mineral oil. The main objective of this work was to verify the possibility to measure crude oil emission spectroscopic without use of volatile solvents. The mixtures of nujol with different -crude oil concentrations were measured with a 10 mm optical path cuvette thus simplifying the fluorescence spectroscopy signal detection. The emission spectra were obtained by exciting the samples with a 400 W Xenon lamp at 350 nm, 450 nm and 532 nm. The emissions of the samples were collected perpendicularly with the excitation axis.     

High purity anatase TiO(2) nanocrystals: near room-temperature synthesis, grain growth kinetics, and surface hydration chemistry

High purity, spherical anatase nanocrystals were prepared by a modified sol-gel method. Mixing of anhydrous TiCl(4) with ethanol at about 0 degrees C yielded a yellowish sol that was transformed into phase-pure anatase of 7.7 nm in size after baking at 87 degrees C for 3 days. This synthesis route eliminates the presence of fine seeds of the nanoscale brookite phase that frequently occurs in low-temperature formation reactions and also significantly retards the phase transformation to rutile at high temperatures. Heating the as-is 7.7 nm anatase for 2 h at temperatures up to 600 degrees C leads to an increase in grain size of the anatase nanoparticles to 32 nm. By varying the calcination time from 2 to 48 h at 300 degrees C, the particle size could be controlled between 12 and 15.3 nm. The grain growth kinetics of anatase nanoparticles was found to follow the equation, D(2) - D(0)(2) = k(0)t(m)e((-)(E)(a)/(RT)) with a time exponent m = 0.286(+/-9) and an activation energy of E(a) = 32 +/- 2 kJ x mol(-)(1). Thermogravimetric analysis in combination with infrared and X-ray photoemission spectroscopies has shown the anatase nanocrystals at different sizes to be composed of an interior anatase lattice with surfaces that are hydrogen-bonded to a wide set of energetically nonequivalent groups. With a decrease in particle size, the anatase lattice volume contracts, while the surface hydration increases. The removal of the surface hydration layers causes coarsening of the nanoparticles.     

Vibrational analysis of polyethylene terephthalate and its deuterated derivatives

The Vibrational analysis of polyethylene terephthalate, polyethylene-d₄ terephthalate, and polyethylene terephthalate-d₄ has been carried out using a valence force field calculated from the infrared and Raman spectra of a series of low molecular weight aromatic esters. The Raman spectra for polyethylene-d₄ terephthalate and polyethylene terephthalate-d₄ are presented and band assignments for these compounds and polyethylene terephthalate are discussed.     

Responsive hydrogels from the intramolecular folding and self-assembly of a designed peptide

A general peptide design is presented that links the pH-dependent intramolecular folding of beta-hairpin peptides to their propensity to self-assemble, affording hydrogels rich in beta-sheet. Chemical responsiveness has been specifically engineered into the material by linking intramolecular folding to changes in solution pH, and mechanical responsiveness, by linking hydrogelation to self-assembly. Circular dichroic and infrared spectroscopies show that at low pH individual peptides are unstructured, affording a low-viscosity aqueous solution. Under basic conditions, intramolecular folding takes place, affording amphiphilic beta-hairpins that intermolecularly self-assemble. Rheology shows that the resulting hydrogel is rigid but is shear-thinning. However, quick mechanical strength recovery after cessation of shear is observed due to the inherent self-assembled nature of the scaffold. Characterization of the gelation process, from the molecular level up through the macroscopic properties of the material, suggests that by linking the intramolecular folding of small designed peptides to their ability to self-assemble, responsive materials can be prepared. Cryo-transmission electron and laser scanning confocal microscopies reveal a water-filled porous scaffold on both the nano- and microscale. The environmental responsiveness, morphology, and peptidic nature make this hydrogel a possible material candidate for biomedical and engineering technology.     

Spectral Properties of Interval Exchange Maps

 In [7], Nogueira and Rudolph proved that for irreducible permutations not of rotation class almost every (a.e.) interval exchange transformation (i.e.t.) is topological weak mixing. It is conjectured that the claim holds if topological weak mixing is replaced by weak mixing. Here we study the behaviour of eigenfunctions of i.e.t. Our analysis gives alternative proofs of results due to Katok and Stepin [4] and Veech [10]: for certain permutations a.e. i.e.t. is weak mixing and for irreducible permutations a.e. i.e.t. is totally ergodic. (Received 1 February 2001)     

Synthesis of substituted α,β-unsaturated δ-lactones from vinyl tellurides

A new approach for the synthesis of α,β-unsaturated δ-lactones, a unit present in many natural products with interesting biological activities is described. The approach was based on the use of a vinyl telluride, and it is complementary to the methods using ring-closing metathesis. The sequence was performed in good overall yield with retention of the Z-double bond geometry.     

Evaluation of the synergetic radio-chemotherapy effects of the radio labelled cisplatin for the treatment of glioma

The proposal of this work was to investigate the effect of the radioactive (NH₃)₂PtCl₂, cis-diamminedichloroplatinum (II) or CDDP* on malignant glioma cells and verify if the low-dose continuous internal radio-chemotherapy would be able to produce additive effects. The antitumoral activity of CDDP* and the non labeled cisplatin, CDDP, were evaluated in glioblastoma. Cisplatin was cytotoxic for glioblastoma cells in a dose dependent manner. Treatment with CDDP*, (IC₅₀ = 1.75 ± 0.07 μM), proved to be more potent than using just CDDP, (IC₅₀ = 4.96 ± 0.40 μM). These results suggest that cisplatin is a very potent radiosensitizer evoking a supra additive effect. Internal radio-chemotherapy treatment based on CDDP* may be useful alternative to reduce the drug concentration required for effective inhibition of glioblastoma growth.