Suppressing grazing chaos in impacting system by structural nonlinearity

In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing. (C) 2007 Elsevier Ltd. All rights reserved.

THE EFFECT of WEAK DISSIPATION IN TWO-DIMENSIONAL MAPPING

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

On a Nonideal (MRD) Damper-Electro-mechanical Absorber Dynamics

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

CRITICAL EXPONENTS and SCALING PROPERTIES FOR THE CHAOTIC DYNAMICS of A PARTICLE IN A TIME-DEPENDENT POTENTIAL BARRIER

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

On chaotic behavior of a fixed offshore structure

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

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.

Solitons in Bose-Einstein condensates trapped in a double-well potential

We investigate, analytically and numerically, families of bright solitons in a system of two linearly coupled nonlinear Schrodinger/Gross-Pitaevskii equations, describing two Bose-Einstein condensates trapped in an asymmetric double-well potential, in particular, when the scattering lengths in the condensates have arbitrary magnitudes and opposite signs. The solitons are found to exist everywhere where they are permitted by the dispersion law. Using the Vakhitov-Kolokolov criterion and numerical methods, we show that, except for small regions in the parameter space, the solitons are stable to small perturbations. Some of them feature self-trapping of almost all the atoms in the condensate with no atomic interaction or weak repulsion is coupled to the self-attractive condensate. An unusual bifurcation is found, when the soliton bifurcates from the zero solution with vanishing amplitude and width simultaneously diverging but at a finite number of atoms in the soliton. By means of numerical simulations, it is found that, depending on values of the parameters and the initial perturbation, unstable solitons either give rise to breathers or completely break down into incoherent waves (radiation). A version of the model with the self-attraction in both components, which applies to the description of dual-core fibers in nonlinear optics, is considered too, and new results are obtained for this much studied system. (C) 2003 Elsevier B.V. All rights reserved.

Macro- and microstructure of the superior cervical ganglion in dogs, cats and horses during maturation

The superior cervical ganglion (SCG) provides sympathetic input to the head and neck, its relation with mandible, submandibular glands, eyes (second and third order control) and pineal gland being demonstrated in laboratory animals. In addition, the SCG's role in some neuropathies can be clearly seen in Horner's syndrome. In spite of several studies published involving rats and mice, there is little morphological descriptive and comparative data of SCG from large mammals. Thus, we investigated the SCG's macro- and microstructural organization in medium (dogs and cats) and large animals (horses) during a very specific period of the post-natal development, namely maturation (from young to adults). The SCG of dogs, cats and horses were spindle shaped and located deeply into the bifurcation of the common carotid artery, close to the distal vagus ganglion and more related to the internal carotid artery in dogs and horses, and to the occipital artery in cats. As to macromorphometrical data, that is ganglion length, there was a 23.6% increase from young to adult dogs, a 1.8% increase from young to adult cats and finally a 34% increase from young to adult horses. Histologically, the SCG's microstructure was quite similar between young and adult animals and among the 3 species. The SCG was divided into distinct compartments (ganglion units) by capsular septa of connective tissue. Inside each ganglion unit the most prominent cellular elements were ganglion neurons, glial cells and small intensely fluorescent cells, comprising the ganglion's morphological triad. Given this morphological arrangement, that is a summation of all ganglion units, SCG from dogs, cats and horses are better characterized as a ganglion complex rather than following the classical ganglion concept. During maturation (from young to adults) there was a 32.7% increase in the SCG's connective capsule in dogs, a 25.8% increase in cats and a 33.2% increase in horses. There was an age-related increase in the neuronal profile size in the SCG from young to adult animals, that is a 1.6-fold, 1.9-fold and 1.6-fold increase in dogs, cats and horses, respectively. on the other hand, there was an age-related decrease in the nuclear profile size of SCG neurons from young to adult animals (0.9-fold, 0.7-fold and 0.8-fold in dogs, cats and horses, respectively). Ganglion connective capsule is composed of 2 or 3 layers of collagen fibres in juxtaposition and, as observed in light microscopy and independently of the animal's age, ganglion neurons were organised in ganglionic units containing the same morphological triad seen in light microscopy. Copyright (c) 2007 S. Karger AG, Basel.

Elasto-plastic structural stability of arches

The elastic-plastic structural stability behaviour of arches is analysed in the present work.The application of the developed mathematical model, allows to determine the elastic-plastic equilibrium paths, looking for critical points, bifurcation or limit, along those paths, associated to the critical load, in case it comes to happen.The equilibrium paths in the elastic-plastic behaviour when compared with the paths in the linear elastic behaviour, may show that, due to influence of the material plasticity, modifications paths appear and consequently alterations in the values of its critical loads.

Hopf-zero bifurcations of reversible vector fields

We study the dynamics of a class of reversible vector fields having eigenvalues (0, alphai, -alphai) around their symmetric equilibria. We give a complete list of all normal forms for such vector fields, their versal unfoldings, and the corresponding bifurcation diagrams of the codimensional-one case. We also obtain some important conclusions on the existence of homoclinic and heteroclinic orbits, invariant tori and symmetric periodic orbits.

Using transient and steady state considerations to investigate the mechanism of loss of stability of a dynamical system

This work presents the complete set of features for solutions of a particular non-ideal mechanical system near the fundamental and near to a secondary resonance region. The system comprises a pendulum with a horizontally moving suspension point. Its motion is the result of a non-ideal rotating power source (limited power supply), acting oil the Suspension point through a crank mechanism. Main emphasis is given to the loss of stability, which occurs by a sequence of events, including intermittence and crisis, when the system reaches a chaotic attractor. The system also undergoes a boundary-crisis, which presents a different aspect in the bifurcation diagram due to the non-ideal supposition. (c) 2004 Published by Elsevier B.V.

The defocusing mechanism of isochronous resonances

We present a numerical study concerning the defocusing mechanism of isochronous resonance island chains in the presence of two permanent robust tori. The process is initialized and concluded through bifurcations of fixed points located on the robust tori. Our approach is based on a Hamiltonian system derived from the resonant normal form. Choosing a convenient parameter in this system, we are able to depict a comprehensive analysis of the dynamics of the problem. (c) 2004 Elsevier B.V. All rights reserved.

On the limit cycles of a class of piecewise linear differential systems in R-4 with two zones

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

Fiber fermentability effects on energy and macronutrient digestibility, fecal traits, postprandial metabolite responses, and colon histology of overweight cats

Considering the different potential benefits of divergent fiber ingredients, the effect of 3 fiber sources on energy and macronutrient digestibility, fermentation product formation, postprandial metabolite responses, and colon histology of overweight cats (Felis catus) fed kibble diets was compared. Twenty-four healthy adult cats were assigned in a complete randomized block design to 2 groups of 12 animals, and 3 animals from each group were fed 1 of 4 of the following kibble diets: control (CO; 11.5% dietary fiber), beet pulp (BP; 26% dietary fiber), wheat bran (WB; 24% dietary fiber), and sugarcane fiber (SF; 28% dietary fiber). Digestibility was measured by the total collection of feces. After 16 d of diet adaptation and an overnight period without food, blood glucose, cholesterol, and triglyceride postprandial responses were evaluated for 16 h after continued exposure to food. on d 20, colon biopsies of the cats were collected under general anesthesia. Fiber addition reduced food energy and nutrient digestibility. of all the fiber sources, SF had the least dietary fiber digestibility (P < 0.05), causing the largest reduction of dietary energy digestibility (P < 0.05). The greater fermentability of BP resulted in reduced fecal DM and pH, greater fecal production [g/(cat x d); as-is], and greater fecal concentration of acetate, propionate, and lactate (P < 0.05). For most fecal variables, WB was intermediate between BP and SF, and SF was similar to the control diet except for an increased fecal DM and firmer feces production for the SF diet (P < 0.05). Postprandial evaluations indicated reduced mean glucose concentration and area under the glucose curve in cats fed the SF diet (P < 0.05). Colon mucosa thickness, crypt area, lamina propria area, goblet cell area, crypt mean size, and crypt in bifurcation did not vary among the diets. According to the fiber solubility and fermentation rates, fiber sources can induce different physiological responses in cats, reduce energy digestibility, and favor glucose metabolism (SF), or improve gut health (BP).