Invariant Measures for Cherry Flows

We investigate the invariant probability measures for Cherry flows, i.e. flows on the two-torus which have a saddle, a source, and no other fixed points, closed orbits or homoclinic orbits. In the case when the saddle is dissipative or conservative we show that the only invariant probability measures are the Dirac measures at the two fixed points, and the Dirac measure at the saddle is the physical measure. In the other case we prove that there exists also an invariant probability measure supported on the quasi-minimal set, we discuss some situations when this other invariant measure is the physical measure, and conjecture that this is always the case. The main techniques used are the study of the integrability of the return time with respect to the invariant measure of the return map to a closed transversal to the flow, and the study of the close returns near the saddle.     

Markov partition in non-hyperbolic interval dynamics

We considerC ² unimodal mapsf such that all periodic points are hyperbolic, the critical point is non-degenerated and non-recurrent, and the Julia set does not contain intervals. We construct a Markov partition for a big part of the Julia set. Then we use it to estimate the limit capacity and Hausdorff dimension of the Julia set.Partially supported by CNPq, S.C.T.-Brazil     

The Role of the Eu<Superscript>3+</Superscript> Concentration on the SrMoO<Subscript>4</Subscript>:Eu Phosphor Properties: Synthesis,Characterization and Photophysical Studies

SrMoO₄ doped with rare earth are still scarce nowadays and have attracted great attention due to their applications as scintillating materials in electro-optical like solid-state lasers and optical fibers, for instance. In this work Sr_1−xEu_xMoO₄ powders, where x = 0.01; 0.03 and 0.05, were synthesized by Complex Polymerization (CP) Method. The structural and optical properties of the SrMoO₄:Eu³⁺ were analyzed by powder X-ray diffraction patterns, Fourier Transform Infra-Red (FTIR), Raman Spectroscopy, and through Photoluminescent Measurements (PL). Only a crystalline scheelite-type phase was obtained when the powders were heat-treated at 800 °C for 2 h, 2θ = 27.8° (100% peak). The excitation spectra of the SrMoO₄:Eu³⁺ (λ_Em. = 614 nm) presented the characteristic band of the Eu^3 + 5L₆ transition at 394 nm and a broad band at around 288 nm ascribed to the charge-transfer from the O (2p) state to the Mo (4d) one in the SrMoO₄ matrix. The emission spectra of the SrMoO₄:Eu³⁺ powders (λ_Exc. = 394 and 288 nm) show the group of sharp emission bands among 523–554 nm and 578–699 nm, assigned to the ⁵D₁→⁷F_{0,1and 2} and ⁵D₀→⁷F_{0,1,2,3 and 4}, respectively. The band related to the ⁵D₀→⁷F₀ transition indicates the presence of Eu³⁺ site without inversion center. This hypothesis is strengthened by the fact that the band referent to the ⁵D₀→⁷F₂ transition is the most intense in the emission spectra.     

Synthesis and characterization of nanostructured iron compounds prepared from the decomposition of iron pentacarbonyl dispersed into carbon materials with varying porosities

This work describes the production and characterization of carbon-iron nanocomposites obtained from the decomposition of iron pentacarbonyl (Fe(CO)₅) mixed with different carbon materials: a high surface area activated carbon (AC), powdered graphite (G), milled graphite (MG), and carbon black (CB). The nanocomposites were prepared either under argon or in ambient atmosphere, with a fixed ratio of Fe(CO)₅ (4.0 mL) to carbon precursor (2.0 g). The images of scanning electron microscopy and the analysis of textural properties indicated the presence of nanostructured Fe compounds homogeneously dispersed into the different classes of pores of the carbon matrices. The elemental Fe content was always larger for samples prepared in ambient atmosphere, reaching values in the range of 20–32 wt%. On the other hand, samples prepared under argon showed reduced Fe content, with values in the range 5–10 wt% for samples prepared from precursors with low surface area (G, MG, and CB) and a much higher value (~19 wt%) for samples prepared from the precursor of high surface area (AC). Mössbauer spectroscopy and X-ray diffractometry showed that the nanoparticles were mostly composed of iron oxides in the case of the samples prepared in oxygen-rich ambient atmosphere and also for the AC-derived nanocomposite prepared under argon, which is consistent with the large oxygen content of this precursor. For the other precursors, with reduced or no oxygen content, metallic iron and iron carbides were found to be the dominant phases in samples prepared under oxygen-free atmosphere. The samples prepared in ambient atmosphere and the AC-derived sample prepared under argon exhibited superparamagnetic behavior at room temperature, as revealed by temperature-dependent magnetization curves and Mössbauer spectroscopy.     

Influence of the deGennes extrapolation parameter on the resistive state of a superconducting strip

We studied the resistive state of a mesoscopic superconducting strip (bridge) at zero external applied magnetic field under a transport electric current, $J_a$, subjected to different types of boundary conditions. The current is applied through a metallic contact (electrode) and the boundary conditions are simulated via the deGennes extrapolation length b. It will be shown that the characteristic current–voltage curve follows a scaling law for different values of b. We also show that the value of $J_a$ at which the first vortex–antivortex (V–Av) pair penetrates the sample, as well as their average velocities and dynamics, strongly depend on the b values. Our investigation was carried out by solving the two-dimensional generalized time dependent Ginzburg–Landau (GTDGL) equation.     

Boundary crisis and transient in a dissipative relativistic standard map

Some dynamical properties for a problem concerning the acceleration of particles in a wave packet are studied. The model is described in terms of a two-dimensional nonlinear map obtained from a Hamiltonian which describes the motion of a relativistic standard map. The phase space is mixed in the sense that there are regular and chaotic regions coexisting. When dissipation is introduced, the property of area preservation is broken and attractors emerge. We have shown that a tiny increase of the dissipation causes a change in the phase space. A chaotic attractor as well as its basin of attraction are destroyed thereby leading the system to experience a boundary crisis. We have characterized such a boundary crisis via a collision of the chaotic attractor with the stable manifold of a saddle fixed point. Once the chaotic attractor is destroyed, a chaotic transient described by a power law with exponent −1 is observed.     

Shrimp-shape domains in a dissipative kicked rotator

Some dynamical properties for a dissipative kicked rotator are studied. Our results show that when dissipation is taken into account a drastic change happens in the structure of the phase space in the sense that the mixed structure is modified and attracting fixed points and chaotic attractors are observed. A detailed numerical investigation in a two-dimensional parameter space based on the behavior of the Lyapunov exponent is considered. Our results show the existence of infinite self-similar shrimp-shaped structures corresponding to periodic attractors, embedded in a large region corresponding to the chaotic regime.     

A peculiar Maxwell’s Demon observed in a time-dependent stadium-like billiard

The dynamics of a driven stadium-like billiard is considered using the formalism of discrete mappings. The model presents a resonant velocity that depends on the rotation number around fixed points and external boundary perturbation which plays an important separation rule in the model. We show that particles exhibiting Fermi acceleration (initial velocity is above the resonant one) are scaling invariant with respect to the initial velocity and external perturbation. However, initial velocities below the resonant one lead the particles to decelerate therefore unlimited energy growth is not observed. This phenomenon may be interpreted as a specific Maxwell’s Demon which may separate fast and slow billiard particles.     

Stable colloidal suspensions of nanostructured zirconium oxide synthesized by hydrothermal process

Nanocrystalline zirconium oxide was synthesized by hydrothermal treatment of ZrO(NO₃)₂ and ZrOCl₂ aqueous solutions at different temperatures and time in presence of hydrogen peroxide. Hydrothermal treatment of zirconium salts (0.25 and 0.50 mol L^?1) produced nanocrystalline monoclinic ZrO₂ powders with narrow size distribution, which were formed by the attachment of the smaller particles with crystallites size of 3.5 nm, estimated by means of the Scherrer’s equation and confirmed by transmission electronic microscopy. Typical monoclinic zirconium oxide X-ray powder diffraction patterns and Raman spectra were obtained for all the crystalline powders. It was observed that the crystallization depends strongly on the temperature, resulting in amorphous material when the synthesis was realized at 100 °C, and crystalline with monoclinic phase when synthesized at 110 °C, independently of the salt used. Zirconium oxide colloidal nanoparticles were formed only at hydrothermal treatments longer than 24 h. The stability of the colloids was successfully characterized of zeta potential, showing an initial value of + 59.2 mV in acid media and isoelectric point at pH = 5.2, in good agreement with previous studies.