Some remarks on bifurcation analysis of a nonlinear vibrating system excited by a shape memory alloy material (SMA)

In this paper, the dynamical response of a coupled oscillator is investigated, taking in consideration the nonlinear behavior of a SMA spring coupling the two oscillators. Due to the nonlinear coupling terms, the system exhibits both regular and chaotic motions. The Poincaré sections for different sets of coupling parameters are verified. © 2011 World Scientific Publishing Company.

On the dynamic behaviour of a nonlinear system weakly connected to a linear single degree-of-freedom system

This paper discusses the dynamic behaviour of a nonlinear two degree-of-freedom system consisting of a harmonically excited linear oscillator weakly connected to a nonlinear attachment that behaves as a hardening Duffing oscillator. A system which behaves in this way could be a shaker (linear system) driving a nonlinear isolator. The mass of the nonlinear system is taken to be much less than that in the linear system and thus the nonlinear system has little effect on the dynamics of the linear system. Of particular interest is the situation when the linear natural frequency of the nonlinear system is less than the natural frequency of the linear system such that the frequency response curve of the nonlinear system bends to higher frequencies and thus interacts with the resonance frequency of the linear system. It is shown that for some values of the system parameters a complicated frequency response curve for the nonlinear system can occur; closed detached curves can appear as a part of the overall amplitude-frequency response. The reason why these detached curves appear is presented and approximate analytical expressions for the jump-up and jump-down frequencies of the system under investigation are given.

One-dimensional Fermi accelerator model with moving wall described by a nonlinear van der Pol oscillator

A modification of the one-dimensional Fermi accelerator model is considered in this work. The dynamics of a classical particle of mass m, confined to bounce elastically between two rigid walls where one is described by a nonlinear van der Pol type oscillator while the other one is fixed, working as a reinjection mechanism of the particle for a next collision, is carefully made by the use of a two-dimensional nonlinear mapping. Two cases are considered: (i) the situation where the particle has mass negligible as compared to the mass of the moving wall and does not affect the motion of it; and (ii) the case where collisions of the particle do affect the movement of the moving wall. For case (i) the phase space is of mixed type leading us to observe a scaling of the average velocity as a function of the parameter (χ) controlling the nonlinearity of the moving wall. For large χ, a diffusion on the velocity is observed leading to the conclusion that Fermi acceleration is taking place. On the other hand, for case (ii), the motion of the moving wall is affected by collisions with the particle. However, due to the properties of the van der Pol oscillator, the moving wall relaxes again to a limit cycle. Such kind of motion absorbs part of the energy of the particle leading to a suppression of the unlimited energy gain as observed in case (i). The phase space shows a set of attractors of different periods whose basin of attraction has a complicated organization. © 2013 American Physical Society.

A simple derivation of the Lindblad equation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Local attractors, degeneracy and analyticity: Symmetry effects on the locally coupled Kuramoto model

In this work we study the local coupled Kuramoto model with periodic boundary conditions. Our main objective is to show how analytical solutions may be obtained from symmetry assumptions, and while we proceed on our endeavor we show apart from the existence of local attractors, some unexpected features resulting from the symmetry properties, such as intermittent and chaotic period phase slips, degeneracy of stable solutions and double bifurcation composition. As a result of our analysis, we show that stable fixed points in the synchronized region may be obtained with just a small amount of the existent solutions, and for a class of natural frequencies configuration we show analytical expressions for the critical synchronization coupling as a function of the number of oscillators, both exact and asymptotic. © 2013 Elsevier Ltd. All rights reserved.

Low-temperature structural effects in the (TMTSF)2PF6 and AsF6 Bechgaard salts

We present a detailed low-temperature investigation of the statics and dynamics of the anions and methyl groups in the organic conductors (TMTSF) 2PF6 and (TMTSF)2AsF6 (TMTSF: tetramethyl-tetraselenafulvalene). The 4 K neutron-scattering structure refinement of the fully deuterated (TMTSF)2PF6-D12 salt allows locating precisely the methyl groups at 4 K. This structure is compared to the one of the fully hydrogenated (TMTSF)2PF6-H12 salt previously determined at the same temperature. Surprisingly, it is found that deuteration corresponds to the application of a negative pressure of 5×102 MPa to the H12 salt. Accurate measurements of the Bragg intensity show anomalous thermal variations at low temperature both in the deuterated PF 6 and AsF6 salts. Two different thermal behaviors have been distinguished. Small Bragg-angle measurements reflect the presence of low-frequency modes at characteristic energies θE = 8.3 K and θE = 6.7 K for the PF6-D12 and AsF6-D12 salts, respectively. These modes correspond to the low-temperature methyl group motion. Large Bragg-angle measurements evidence an unexpected structural change around 55 K, which probably corresponds to the linkage of the anions to the methyl groups via the formation of F...D-CD2 bonds observed in the 4 K structural refinement. Finally we show that the thermal expansion coefficient of (TMTSF)2PF6 is dominated by the librational motion of the PF6 units. We quantitatively analyze the low-temperature variation of the lattice expansion via the contribution of Einstein oscillators, which allows us to determine for the first time the characteristic frequency of the PF6 librations: θE ≈ 50 K and θE = 76 K for the PF6-D12 and PF6-H12 salts, respectively. © 2013 American Physical Society.

Projeto de um oscilador controlado por corrente com configuração em anel, tecnologia CMOS e melhoria no ruído de fase

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dinâmica caótica e sincronização de fase em mapas acoplados

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Um estudo do efeito da composição dos vidros teluretos sobre os índices de refração linear e não linear

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Um estudo da dinâmica fracamente não-linear de um sistema nanomecânico

Pós-graduação em Matemática - IBILCE

Estudo de sistemas lineares por parte com três zonas e aplicação na análise de um circuito elétrico envolvendo um memristor

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Modelo vibro-rotacional para a molécula de DNA

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Um estudo sobre sincronização no modelo de Kuramoto

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

O princípio de ação quântica de Schwinger: aspectos do tratamento de sistemas dependentes do tempo e interagentes

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Long-Lasting Oscillations in the Electro-Oxidation of Formic Acid on PtSn Intermetallic Surfaces

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)