Characterization of Stability Region for General Autonomous Nonlinear Dynamical Systems

The existing characterization of stability regions was developed under the assumption that limit sets on the stability boundary are exclusively composed of hyperbolic equilibrium points and closed orbits. The characterizations derived in this technical note are a generalization of existing results in the theory of stability regions. A characterization of the stability boundary of general autonomous nonlinear dynamical systems is developed under the assumption that limit sets on the stability boundary are composed of a countable number of disjoint and indecomposable components, which can be equilibrium points, closed orbits, quasi-periodic solutions and even chaotic invariant sets.

TYPE-ZERO SADDLE-NODE BIFURCATIONS AND STABILITY REGION ESTIMATION OF NONLINEAR AUTONOMOUS DYNAMICAL SYSTEMS

A complete characterization of the stability boundary of a class of nonlinear dynamical systems that admit energy functions is developed in this paper. This characterization generalizes the existing results by allowing the type-zero saddle-node nonhyperbolic equilibrium points on the stability boundary. Conceptual algorithms to obtain optimal estimates of the stability region (basin of attraction) in the form of level sets of a given family of energy functions are derived. The behavior of the stability region and the corresponding estimates are investigated for parameter variation in the neighborhood of a type-zero saddle-node bifurcation value.

Central pain due to stroke: cognitive representation and coping according to gender

Objective: To identify and compare perceptions of pain and how it is faced between men and women with central post-stroke pain. Methods: The participants were 25 men and 25 women of minimum age 30 years-old and minimum schooling level of four years, presenting central post-stroke pain for at least three months. The instruments used were: Mini-Mental State Examination; structured interview for the Brief Psychiatric Scale; Survey of Sociodemographic and Clinical Data; Visual Analogue Scale (VAS); Ways of Coping with Problems Scale (WCPS) in Scale; Revised Illness Perception Questionnaire (IPQ-R); and Beck Depression Inventory (BD). Results: A significantly greater number of women used the coping strategy "Turn to spiritual and religious activities" in WCPS. They associated their emotional state with the cause of pain in IPQ-R. "Distraction of attention" was the strategy most used by the subjects. Conclusion: Women used spiritual and religious activities more as a coping strategy and perceived their emotional state as the cause of pain.

Dynamical changes from harmonic vibrations of a limited power supply driving a Duffing oscillator

The harmonic oscillations of a Duffing oscillator driven by a limited power supply are investigated as a function of the alternative strength of the rotor. The semi-trivial and non-trivial solutions are derived. We examine the stability of these solutions and then explore the complex behaviors associated with the bifurcations sequences. Interestingly, a 3D diagram provides a global view of the effects of alternate strength on the appearance of chaos and hyperchaos on the system.

DYNAMICAL EVOLUTION OF VISCOUS DISKS AROUND Be STARS. I. PHOTOMETRY

Be stars possess gaseous circumstellar disks that modify in many ways the spectrum of the central B star. Furthermore, they exhibit variability at several timescales and for a large number of observables. Putting the pieces together of this dynamical behavior is not an easy task and requires a detailed understanding of the physical processes that control the temporal evolution of the observables. There is an increasing body of evidence that suggests that Be disks are well described by standard alpha-disk theory. This paper is the first of a series that aims at studying the possibility of inferring several disk and stellar parameters through the follow-up of various observables. Here we study the temporal evolution of the disk density for different dynamical scenarios, including the disk buildup as a result of a long and steady mass injection from the star, the disk dissipation that occurs after mass injection is turned off, as well as scenarios in which active periods are followed by periods of quiescence. For those scenarios, we investigate the temporal evolution of continuum photometric observables using a three-dimensional non-LTE radiative transfer code. We show that light curves for different wavelengths are specific of a mass loss history, inclination angle, and alpha viscosity parameter. The diagnostic potential of those light curves is also discussed.

Dynamical Elastic Moduli of the Ti-13Nb-13Zr biomaterial alloy by mechanical spectroscopy

Dynamical Elastic Moduli of the Ti-13Nb-13Zr biomaterial alloy were obtained using the mechanical spectroscopy technique. The sample with heat treatment at 1170K for 30 minutes and water quenched with subsequent aging treatment at 670 K for 3 hours (TNZ + WQ + 670 K/3 h), was characterized through decay of free oscillations of the sample in the flexural vibration mode. The spectra of anelastic relaxation (internal friction and frequency) in the temperature range from 300 K to 625 K not revealed the presence of relaxation process. As shown in the literature, the hcp structure usually does not exhibit any relaxation due to the symmetry of the sites in the crystalline lattice, but if there is some relaxation, this only occurs in special cases such as low concentration of zirconium or saturation of the stoichiometric ratio of oxygen for zirconium. Dynamical elastic modulus obtained for TNZ + WQ + 670 K/3 h alloy was 87 GPa at room temperature, which is higher than the value for Ti-13Nb-13Zr alloy (64 GPa) of the literature. This increment may be related to the change of the proportion of α and β phases. Besides that, the presence of precipitates in the alloy after aging treatment hardens the material and reduces its ductility.

Stability boundary characterization of nonlinear autonomous dynamical systems in the presence of saddle-node equilibrium points

A dynamical characterization of the stability boundary for a fairly large class of nonlinear autonomous dynamical systems is developed in this paper. This characterization generalizes the existing results by allowing the existence of saddle-node equilibrium points on the stability boundary. The stability boundary of an asymptotically stable equilibrium point is shown to consist of the stable manifolds of the hyperbolic equilibrium points on the stability boundary and the stable, stable center and center manifolds of the saddle-node equilibrium points on the stability boundary.

Determination of dynamical and physical parameters of the system CoRoT 3

The two main tools to determine the dynamical and physical parameters of exoplanet systems are the radial velocity (RV) measurements and, when available, transit timings. The two techniques are complementary: The RV's allow us to know some of the orbital elements while the transit timings allow us to obtain the orbital inclination and planetary radius, impossible of obtain from the RV, and to resolve the indetermination in the determination of the planet mass from the RV's. The space observation of transiting planets is however not limited to transit times. They extend to long periods of time and are precise enough to provide information on variations along the orbit. Besides the effects of stellar rotation, deserve mention the Doppler shift in the radiation flux, as consequence of stellar movement around the center of mass, or Beaming Effect (BE); the Ellipsoidal Variability (EV) due to the tidal deformation of the star due to the gravitation of its close companion; and the Reflection (ER) of the stellar radiation incident on the planet and re-emitted to the observer. In the case of large hot Jupiters, these effects are enhanced by the strong gravitational interaction and the analysis of the light variation allows us independent estimates of the mass and radius of planet. The planetary system CoRoT 3 is favorable for such analysis. In this case, the secondary is a brown dwarf whose mass is of the order of 22Mj. We show results obtained from the analysis of 35 RV measurements, 236999 photometric observations and 11 additional RV observations made during a transit to determine the star rotation via the Rossiter-McLaughlin effect. The results obtained from this determination are presented in this communication. The results are compared to those resulting from other determinations.

Dynamical speckles patterns of action potential transmission effects in squid giant axon membrane.

Undoubtedly the most important result of the investigations in physiology and biophysics was the discovery of the electrochemical mechanism of propagation of the action potential in nerves that was made by Hodgkin and Huxley during the first half of the past century. Since some decades ago diverse experiments about the electro optical properties of the axon membrane there was published using the most diverse optical experimental ‘procedures POT 6-10’. In this paper some results of a dynamical speckle technique applied for obtaining microscopic images of a section of a squid giant axon membrane during the activation by electrical impulses and his digital process are presented.

Ontology for Data Representation in the Production of Cotton Fiber in Brazil

An important feature in computer systems developed for the agricultural sector is to satisfy the heterogeneity of data generated in different processes. Most problems related with this heterogeneity arise from the lack of standard for different computing solutions proposed. An efficient solution for that is to create a single standard for data exchange. The study on the actual process involved in cotton production was based on a research developed by the Brazilian Agricultural Research Corporation (EMBRAPA) that reports all phases as a result of the compilation of several theoretical and practical researches related to cotton crop. The proposition of a standard starts with the identification of the most important classes of data involved in the process, and includes an ontology that is the systematization of concepts related to the production of cotton fiber and results in a set of classes, relations, functions and instances. The results are used as a reference for the development of computational tools, transforming implicit knowledge into applications that support the knowledge described. This research is based on data from the Midwest of Brazil. The choice of the cotton process as a study case comes from the fact that Brazil is one of the major players and there are several improvements required for system integration in this segment.

From inflation to dark energy through a dynamical Λ: an attempt at alleviating fundamental cosmic puzzles

After decades of successful hot big-bang paradigm, cosmology still lacks a framework in which the early inflationary phase of the universe smoothly matches the radiation epoch and evolves to the present “quasi” de Sitter spacetime. No less intriguing is that the current value of the effective vacuum energy density is vastly smaller than the value that triggered inflation. In this paper, we propose a new class of cosmologies capable of overcoming, or highly alleviating, some of these acute cosmic puzzles. Powered by a decaying vacuum energy density, the spacetime emerges from a pure nonsingular de Sitter vacuum stage, “gracefully” exits from inflation to a radiation phase followed by dark matter and vacuum regimes, and, finally, evolves to a late-time de Sitter phase.

A model and an algebra for semi-structured and full-text queries

The need for a convergence between semi-structured data management and Information Retrieval techniques is manifest to the scientific community. In order to fulfil this growing request, W3C has recently proposed XQuery Full Text, an IR-oriented extension of XQuery. However, the issue of query optimization requires the study of important properties like query equivalence and containment; to this aim, a formal representation of document and queries is needed. The goal of this thesis is to establish such formal background. We define a data model for XML documents and propose an algebra able to represent most of XQuery Full-Text expressions. We show how an XQuery Full-Text expression can be translated into an algebraic expression and how an algebraic expression can be optimized.