A reducing of a chaotic movement to a periodic orbit, of a micro-electro-mechanical system, by using an optimal linear control design

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

Scaling dynamics for a particle in a time-dependent potential well

Some dynamical properties for a classical particle confined in an infinitely deep box of potential containing a periodically oscillating square well are studied. The dynamics of the system is described by using a two-dimensional non-linear area-preserving map for the variables energy and time. The phase space is mixed and the chaotic sea is described using scaling arguments. Scaling exponents are obtained as a function of all the control parameters, extending the previous results obtained in the literature. (c) 2012 Elsevier B.V. All rights reserved.

Phase-Locked loops lock-in range in Frequency Modulated-Atomic Force Microscope nonlinear control system

Since the mid 1980s the Atomic Force Microscope is one the most powerful tools to perform surface investigation, and since 1995 Non-Contact AFM achieved true atomic resolution. The Frequency-Modulated Atomic Force Microscope (FM-AFM) operates in the dynamic mode, which means that the control system of the FM-AFM must force the micro-cantilever to oscillate with constant amplitude and frequency. However, tip-sample interaction forces cause modulations in the microcantilever motion. A Phase-Locked loop (PLL) is used to demodulate the tip-sample interaction forces from the microcantilever motion. The demodulated signal is used as the feedback signal to the control system, and to generate both topographic and dissipation images. As a consequence, a proper design of the PLL is vital to the FM-AFM performance. In this work, using bifurcation analysis, the lock-in range of the PLL is determined as a function of the frequency shift (Q) of the microcantilever and of the other design parameters, providing a technique to properly design the PLL in the FM-AFM system. (C) 2011 Elsevier B.V. All rights reserved.

Dynamics of Enceladus and Dione inside the 2:1 mean-motion resonance under tidal dissipation

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

Instability zones for satellites of asteroids: The example of the (87) Sylvia system

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

On non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin-Huxley (HH) mathematical model

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

On a nonlinear and chaotic non-ideal vibrating system with shape memory alloy (SMA)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The dynamics of a one-dimensional parabolic problem versus the dynamics of its discretization

In this paper we prove that the spatial discretization of a one dimensional system of parabolic equations. with suitably small step size, contains exactly the same asymptotic dynamics as the continuous problem. (C) 2000 Academic Press.

Dynamics and cytochemistry of oogenesis in Leporinus striatus Kner (Teleostei, Characiformes, Anostomidae) from the Rio Sapucaí, Minas Gerais State, Brazil

Oogenesis involves a sequense of transformations which are undergone by female germ cells. These cells change into oogonias and then into mature oocytes. Sexually mature females were collected monthly, during one year, from the Rio Sapucaí, tributary of the Rio Grande, which is part of the Furnas Reservoir system in the state of Minas Gerais. The observed material showed that oogonias were small spherical cells, had a big spherical nucleus, with a single nucleolus, and weakly stained cytoplasm with eosinophilic granules (FG stained), which indicate their protein content. The primary oocytes showed a big basophilic nucleus, with a large peripheral nucleolus, and several smaller nucleoli. They show a reduced cytoplasmic content. The previtellogenic oocytes presented voluminous cytoplasm and nucleus with several small peripheral nucleoli. The oocytes underwent vitellogenesis with the development of the zona radiata and the follicle cells. The zona radiata had two layers, the outer and the inner, which showed its protein content when stained with CM and FG techniques. TB pH 2.5 and pH 4.0 staining showed that oocytes undergoing vitellogenesis presented weakly stained cytoplasm and peripheral cytoplasmic vesicles. The follicle cells that were squamous became cuboidal. In mature oocytes, the yolk granules that filled the cytoplasm became green and blue when stained with FG and CM techniques, indicating their protein content. The perivitclline region showed rosy stained vesicles (TB pH 2.5 and pH 4.0) spread among the weakly stained peripheral vesicles, which seemed to be the cortical alveoli. The zona radiata cells, CM and FG stained, still showed two layers like the oocytes from the previous stage, but thicker.

Chaotic vibrations of a nonideal electro-mechanical system

Nonideal systems are those in which one takes account of the influence of the oscillatory system on the energy supply with a limited power (Kononenko, 1969). In this paper, a particular nonideal system is investigated, consisting of a pendulum whose support point is vibrated along a horizontal guide by a two bar linkage driven by a DC motor, considered to be a limited power supply. Under these conditions, the oscillations of the pendulum are analyzed through the variation of a control parameter. The voltage supply of the motor is considered to be a reliable control parameter. Each simulation starts from zero speed and reaches a steady-state condition when the motor oscillates around a medium speed. Near the fundamental resonance region, the system presents some interesting nonlinear phenomena, including multi-periodic, quasiperiodic, and chaotic motion. The loss of stability of the system occurs through a saddle-node bifurcation, where there is a collision of a stable orbit with an unstable one, which is approximately located close to the value of the pendulum's angular displacement given by alpha (C)= pi /2. The aims of this study are to better understand nonideal systems using numerical simulation, to identify the bifurcations that occur in the system, and to report the existence of a chaotic attractor near the fundamental resonance. (C) 2001 Elsevier B.V. Ltd. All rights reserved.

The energy landscape for solvent dynamics in electron transfer reactions: A minimalist model

Energy fluctuations of a solute molecule embedded in a polar solvent are investigated to depict the energy landscape for solvation dynamics. The system is modeled by a charged molecule surrounded by two layers of solvent dipolar molecules with simple rotational dynamics. Individual solvent molecules are treated as simple dipoles that can point toward or away from the central charge (Ising spins). Single-spin-flip Monte Carlo kinetics simulations are carried out in a two-dimensional lattice for different central charges, radii of outer shell, and temperatures. By analyzing the density of states as a function of energy and temperatures, we have determined the existence of multiple freezing transitions. Each of them can be associated with the freezing of a different layer of the solvent. (C) 2002 American Institute of Physics.

RELATIVISTIC 3-PARTICLE DYNAMICAL EQUATIONS .2. APPLICATION TO THE TRINUCLEON SYSTEM

We calculate the contribution of relativistic dynamics on the neutron-deutron scattering length and triton binding energy employing five sets trinucleon potential models and four types of three-dimensional relativistic three-body equations suggested in the preceding paper. The relativistic correction to binding energy may vary a lot and even change sign depending on the relativistic formulation employed. The deviations of these observables from those obtained in nonrelativistic models follow the general universal trend of deviations introduced by off- and on-shell variations of two- and three-nucleon potentials in a nonrelativistic model calculation. Consequently, it will be difficult to separate unambiguously the effect of off- and on-shell variations of two- and three-nucleon potentials on low-energy three-nucleon observables from the effect of relativistic dynamics. (C) 1994 Academic Press, Inc.

Biosotption of lanthanum using Sargassum fluitans in batch system

Separation and purification of lanthanum from other rare-earth (RE) elements are highly complex processes comprising several steps of extraction using organic solvents or ion-exchange resins at high costs. In order to study the biosorption process as an alternative for conventional lanthanum recovery, this work investigated some basic aspects of lanthanum-Sargassum biomass interactions in batch equilibrium contact. The dynamics of biosorption, influence of pH, and the desorption of this RE were investigated. Maximum biosorption coefficient (q(max)) increased from 0.05 at pH 2 to 0.53 mmol g(-1) at pH 5 for lanthanum sulfate. When lanthanum chloride was used, a higher q(max) at pH 5 (0.73 mmol g(-1)) was observed as compared to the sulfate salt (q(max) = 0.53 mmol g(-1)) at the same pH. Adsorption and desorption curves pointed out a complete recovery of metal adsorbed in the Sargassum fluitans biomass, showing a reversibility of this process and indicating the potential of biosorption for lanthanum removal and recovery. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Non-local interactions and the dynamics of dispersal in immature insects

A simple mathematical model is developed to explain the appearance of oscillations in the dispersal of larvae from the food source in experimental populations of certain species of blowflies. The life history of the immature stage in these flies, and in a number of other insects, is a system with two populations, one of larvae dispersing on the soil and the other of larvae that burrow in the soil to pupate. The observed oscillations in the horizontal distribution of buried pupae at the end of the dispersal process are hypothesized to be a consequence of larval crowding at a given point in the pupation substrate. It is assumed that dispersing larvae are capable of perceiving variations in density of larvae buried at a given point in the substrate of pupation, and that pupal density may influence pupation of dispersing larvae. The assumed interaction between dispersing larvae and the larvae that are burrowing to pupate is modeled using the concept of non-local effects. Numerical solutions of integro-partial differential equations developed to model density-dependent immature dispersal demonstrate that variation in the parameter that governs the non-local interaction between dispersing and buried larvae induces oscillations in the final horizontal distribution of pupae. (C) 1997 Academic Press Limited.

PHENOMENOLOGICAL APPLICATION OF THE PROJECTION-OPERATOR METHOD AND ITS CONNECTION WITH CRITICAL-DYNAMICS

We consider the dynamics of a system of interacting spins described by the Ginzburg-Landau Hamiltonian. The method used is Zwanzig's version of the projection-operator method, in contrast to previous derivations in which we used Mori's version of this method. It is proved that both methods produce the same answer for the Green's function. We also make contact between the projection-operator method and critical dynamics.