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).

Theoretical Dynamics of Experimental Populations of Introduced and Native Blowflies (Diptera: Calliphoridae)

Equilibrium dynamics in experimental populations of Chrysomya megacephala (F.) and C. putoria (Wiedemann), which have recently invaded the Americas, and the native species Cochliomyia macellaria (F.), were investigated using nonlinear difference equations. A theoretical analysis of the mathematical model using bifurcation theory established the combination of demographic parameters responsible for producing shifts in blowfly population dynamics from stable equilibria to bounded cycles and aperiodic behavior. Mathematical modeling shows that the populations of the 2 introduced Chrysomya species will form stable oscillations with numbers fluctuating 3-4 times in successive generations. However, in the native species C. macellaria, the dynamics is characterized by damping oscillations in population size, leading to a stable population level.

Carbon monoxide oxidation over platinum: Stable, oscillatory and quasi-chaotic regimes

We model the heterogeneously catalyzed oxidation of CO over a Pt surface. A phase diagram analysis is used to probe the several steady state regimes and their stability. We incorporate an experimentally observed 'slow' sub-oxide kinetic step, thereby generalizing a previously presented model. In agreement with experimental data, stable, oscillatory and quasi-chaotic regimes are obtained. Furthermore, the inclusion of the sub-oxide step yields a relaxation oscillation regime. © 1998 Elsevier Science B.V. All rights reserved.

Critical coupling for chiral symmetry breaking in QCD motivated models

We determine the critical coupling constant above which dynamical chiral symmetry breaking occurs in a class of QCD motivated models where the gluon propagator has an enhanced infrared behavior. Using methods of bifurcation theory we find that the critical value of the coupling constant is always smaller than the one obtained for QCD. ©2000 The American Physical Society.

Escape in a nonideal electro-mechanical system

In this work a particular system is investigated consisting of a pendalum whose point of support is vibrated along a horizontal guide by a two bar linkage driven from a DC motor, considered as a limited power source. This system is nonideal since the oscillatory motion of the pendulum influences the speed of the motor and vice-versa, reflecting in a more complicated dynamical process. This work comprises the investigation of the phenomena that appear when the frequency of the pendulum draws near a secondary resonance region, due to the existing nonlinear interactions in the system. Also in this domain due to the power limitation of the motor, the frequency of the pendulum can be captured at resonance modifying completely the final response of the system. This behavior is known as Sommerfield effect and it will be studied here for a nonlinear system.

The dynamics of bright matter wave solitons in a quasi one-dimensional Bose-Einstein condensate with a rapidly varying trap

The dynamics of a bright matter wave soliton in a quasi one-dimensional Bose-Einstein condensate (BEC) with a periodically rapidly varying time trap is considered. The governing equation is based on averaging the fast modulations of the Gross-Pitaevskii (GP) equation. This equation has the form of a GP equation with an effective potential of a more complicated structure than an unperturbed trap. In the case of an inverted (expulsive) quadratic trap corresponding to an unstable GP equation, the effective potential can be stable. For the bounded space trap potential it is showed that bifurcation exists, i.e. the single-well potential bifurcates to the triple-well effective potential. The stabilization of a BEC cloud on-site state in the temporary modulated optical lattice is found. This phenomenon is analogous to the Kapitza stabilization of an inverted pendulum. The analytical predictions of the averaged GP equation are confirmed by numerical simulations of the full GP equation with rapid perturbations.

Behavioural Analysis of a Nonlinear Mechanical System Using Transient Trajectories

This work aims at a better comprehension of the features of the solution surface of a dynamical system presenting a numerical procedure based on transient trajectories. For a given set of initial conditions an analysis is made, similar to that of a return map, looking for the new configuration of this set in the first Poincaré sections. The mentioned set of I.C. will result in a curve that can be fitted by a polynomial, i.e. an analytical expression that will be called initial function in the undamped case and transient function in the damped situation. Thus, it is possible to identify using analytical methods the main stable regions of the phase portrait without a long computational time, making easier a global comprehension of the nonlinear dynamics and the corresponding stability analysis of its solutions. This strategy allows foreseeing the dynamic behavior of the system close to the region of fundamental resonance, providing a better visualization of the structure of its phase portrait. The application chosen to present this methodology is a mechanical pendulum driven through a crankshaft that moves horizontally its suspension point.