Remarks on Parametric Surface Waves in a Nonlinear and Non-Ideally Excited Tank

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Finding critical exponents for two-dimensional Hamiltonian maps

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dissipation as a mechanism of energy gain

Some properties of the annular billiard under the presence of weak dissipation are studied. We show, in a dissipative system, that the average energy of a particle acquires higher values than its average energy of the conservative case. The creation of attractors, associated with a chaotic dynamics in the conservative regime, both in appropriated regions of the phase space, constitute a generic mechanism to increase the average energy of dynamical systems.

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. (C) 2011 American Institute of Physics. [doi:10.1063/1.3657917]

Parameter space for a dissipative Fermi-Ulam model

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

Blocking Radial Diffusion in a Double-Waved Hamiltonian Model

A non-twist Hamiltonian system perturbed by two waves with particular wave numbers can present Robust Tori, barriers created by the vanishing of the perturbing Hamiltonian at some defined positions. When Robust Tori exist, any trajectory in phase space passing close to them is blocked by emergent invariant curves that prevent the chaotic transport. We analyze the breaking up of the RT as well the transport dependence on the wave numbers and on the wave amplitudes. Moreover, we report the chaotic web formation in the phase space and how this pattern influences the transport.

Magnetic Field Line Escape: Comparison with Mean Free Path

In the present work, we determine the fraction of magnetic field lines that reach the tokamak wall leaving the plasma surrounded by a chaotic layer created by resonant perturbations at the plasma edge. The chaotic layer arises in a scenario where an integrable magnetic field with reversed magnetic shear is perturbed by an ergodic magnetic limiter. For each considered line, we calculate its connection length, i.e. the number of toroidal turns that the field lines complete before reaching the wall. We represent the results in the poloidal section in which the initial coordinates are chosen. We also estimate the radial profile of the fraction of field lines, for different temperatures, whose connection lengths are smaller than the electron collisional mean free path.

Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Scaling investigation for the dynamics of charged particles in an electric field accelerator

Some dynamical properties of an ensemble of trajectories of individual (non-interacting) classical particles of mass m and charge q interacting with a time-dependent electric field and suffering the action of a constant magnetic field are studied. Depending on both the amplitude of oscillation of the electric field and the intensity of the magnetic field, the phase space of the model can either exhibit: (i) regular behavior or (ii) a mixed structure, with periodic islands of regular motion, chaotic seas characterized by positive Lyapunov exponents, and invariant Kolmogorov-Arnold-Moser curves preventing the particle to reach unbounded energy. We define an escape window in the chaotic sea and study the transport properties for chaotic orbits along the phase space by the use of scaling formalism. Our results show that the escape distribution and the survival probability obey homogeneous functions characterized by critical exponents and present universal behavior under appropriate scaling transformations. We show the survival probability decays exponentially for small iterations changing to a slower power law decay for large time, therefore, characterizing clearly the effects of stickiness of the islands and invariant tori. For the range of parameters used, our results show that the crossover from fast to slow decay obeys a power law and the behavior of survival orbits is scaling invariant. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4772997]

Principais normas e recomendações existentes para o controle de vibrações provocadas pelo uso de explosivos em áreas urbanas: parte II

As atividades que envolvem o uso de explosivos devem ser controladas, não só com relação ao desmonte de estruturas (rocha e outros materiais), mas também quanto a danos estruturais em edificações próximas (casas, edificações históricas, etc.) e outros impactos ambientais como vibração, propagação de ruídos, ultralançamentos e sobrepressão atmosférica. Tais atividades são regidas por normas técnicas que sugerem parâmetros de medição e limites definidos na avaliação de prováveis danos. No caso específico de minerações em áreas urbanas, a velocidade de vibração de partícula (Vp), normalmente expressa em mm/s, é o parâmetro que tem dado melhor correlação na avaliação de possíveis danos às estruturas civis, atribuídos às vibrações do terreno. As diferentes normas existentes apresentam valores de Vp que variam de 2mm/s para edifícios históricos até 150mm/s para construções em concreto armado. A maioria delas considera na avaliação de danos estruturais, além da velocidade, a freqüência da vibração. Algumas normas foram elaboradas com base em dados experimentais, analisando parâmetros como o tipo de construção e o material nela utilizados, outras se basearam apenas em valores empíricos, mas todas apresentam valores conservativos. A norma brasileira não avalia o parâmetro freqüência e não classifica os diferentes tipos de estruturas civis, restringindo-se ao valor resultante da velocidade de vibração como parâmetro medido, sendo, assim, limitada e deficiente em relação às normas internacionais. A coletânea aqui apresentada reuniu as normas nas Américas e em outros continentes, além de uma comparação com as normas européias mais importantes em âmbito mundial.

Quantum entanglement and fixed point Hopf bifurcation

We present the qualitative differences in the phase transitions of the mono-mode Dicke model in its integrable and chaotic versions. These qualitative differences are shown to be connected to the degree of entanglement of the ground state correlations as measured by the linear entropy. We show that a first order phase transition occurs in the integrable case whereas a second order in the chaotic one. This difference is also reflected in the classical limit: for the integrable case the stable fixed point in phase space undergoes a Hopf type whereas the second one a pitchfork type bifurcation. The calculation of the atomic Wigner functions of the ground state follows the same trends. Moreover, strong correlations are evidenced by its negative parts. (c) 2006 Elsevier B.V. All rights reserved.

Reaction pathway to the synthesis of anatase via the chemical modification of titanium isopropoxide with acetic acid

Anatase nanoparticles were obtained through a modified sol-gel route from titanium isopropoxide modified with acetic acid in order to control hydrolysis and condensation reactions. The modification of Ti(O(i)Pr)(4) with acetic acid reduces the availability of groups that hydrolyze and condense easily through the formation of a stable complex whose structure was determined to be Ti(OCOCH(3))(O(i)Pr)(2) by means of FTIR and (13)C NMR. The presence of this complex was confirmed with FTIR in the early stages of the process. A doublet in 1542 and 1440 cm(-1) stands for the asymmetric and symmetric stretching vibrations of the carboxylic group coordinated to Ti as a bidentate ligand. The gap of 102 cm(-1) between these signals suggests that acetate acts preferentially as a bidentate rather than as a bridging ligand between two titanium atoms. The use of acetic acid as modifier allows the control of both the degree of condensation and oligomerization of the precursor and leads to the preferential crystallization of TiO(2) in the anatase phase. A possible reaction pathway toward the formation of anatase is proposed on the basis of the intermediate species present in a 1:1 Ti(O(i)Pr)(4):CH(3)COOH molar system in which esterification reactions that introduce H(2)O into the reaction mixture were seen to be negligible. The Rietveld refinement and TEM analysis revealed that the powder is composed of isotropic anatase nanocrystallites.

Preparation and characterization of new glassy system As2P2S8-Ga2S3

Glasses having the composition (100 - x)As2P2S8-xGa(2)S(3) with x ranging from 0 to 50% were investigated to determine the compositional effect on properties and local structure. The glass transition temperature (T-g) and the stability parameter against crystallization (T-x - T-g) increased with the addition of Ga2S3. The structure of these glasses was probed by Raman scattering, Fourier transform infrared (FT-IR) and P-31 nuclear magnetic resonance. on the basis of the observed vibrations and the strength of the P-31-P-31 homonuclear magnetic dipolar coupling, two scenarios can be proposed for the structural evolution induced by the addition of Ga2S3. For x <= 20% we may have the formation of GaS4E- groups (E = nonbonding electron), and for x >= 30% we have depolymerization of the As2P2S8 units and the formation of a network of GaPS4 units with each PS4/2 unit (Q(4)) species carrying a single positive formal charge.

Temporal dynamics of stomatal conductance of plants under water deficit: can homeostasis be improved by more complex dynamics?

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