Comments on nonlinear dynamics of a non-ideal Duffing-Rayleigh oscillator: Numerical and analytical approaches

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

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)

Effects of oscillatory behavior of the dipole function on the dissociation dynamics of the classical driven Morse oscillator

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)

Dynamics of a spacecraft and normalization around Lagrangian points in the Neptune-Triton system

The problem of a spacecraft orbiting the Neptune-Triton system is presented. The new ingredients in this restricted three body problem are the Neptune oblateness and the high inclined and retrograde motion of Triton. First we present some interesting simulations showing the role played by the oblateness on a Neptune's satellite, disturbed by Triton. We also give an extensive numerical exploration in the case when the spacecraft orbits Triton, considering Sun, Neptune and its planetary oblateness as disturbers. In the plane a x I (a = semi-major axis, I = inclination), we give a plot of the stable regions where the massless body can survive for thousand of years. Retrograde and direct orbits were considered and as usual, the region of stability is much more significant for the case of direct orbit of the spacecraft (Triton's orbit is retrograde). Next we explore the dynamics in a vicinity of the Lagrangian points. The Birkhoff normalization is constructed around L-2, followed by its reduction to the center manifold. In this reduced dynamics, a convenient Poincare section shows the interplay of the Lyapunov and halo periodic orbits, Lissajous and quasi-halo tori as well as the stable and unstable manifolds of the planar Lyapunov orbit. To show the effect of the oblateness, the planar Lyapunov family emanating from the Lagrangian points and three-dimensional halo orbits are obtained by the numerical continuation method. Published by Elsevier Ltd. on behalf of COSPAR.

Scaling investigation for the dynamics of charged particles in an electric field accelerator

Some dynamical properties of an ensemble of trajectories of individual (non-interacting) classical particles of mass m and charge q interacting with a time-dependent electric field and suffering the action of a constant magnetic field are studied. Depending on both the amplitude of oscillation of the electric field and the intensity of the magnetic field, the phase space of the model can either exhibit: (i) regular behavior or (ii) a mixed structure, with periodic islands of regular motion, chaotic seas characterized by positive Lyapunov exponents, and invariant Kolmogorov-Arnold-Moser curves preventing the particle to reach unbounded energy. We define an escape window in the chaotic sea and study the transport properties for chaotic orbits along the phase space by the use of scaling formalism. Our results show that the escape distribution and the survival probability obey homogeneous functions characterized by critical exponents and present universal behavior under appropriate scaling transformations. We show the survival probability decays exponentially for small iterations changing to a slower power law decay for large time, therefore, characterizing clearly the effects of stickiness of the islands and invariant tori. For the range of parameters used, our results show that the crossover from fast to slow decay obeys a power law and the behavior of survival orbits is scaling invariant. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4772997]

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.

Temporal dynamics of stomatal conductance of plants under water deficit: can homeostasis be improved by more complex dynamics?

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

Temporal dynamics of two species of Chaetophoraceae (Chlorophyta) in tropical streams of São Paulo State, Southeastern Brazil

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

Fluid dynamics of air in a packed bed: velocity profiles and the continuum model assumption

Air flow through packed beds was analyzed experimentally under conditions ranging from those that reinforce the effect of the wall on the void fraction to those that minimize it. The packing was spherical particles, with a tube-to-particle diameter ratio (D/dp) between 3 and 60. Air flow rates were maintained between 1.3 and 4.44 m3/min, and gas velocity was measured with a Pitot tube positioned above the bed exit. Measurements were made at various radial and angular coordinate values, allowing the distribution of air flow across the bed to be described in detail. Comparison of the experimentally observed radial profiles with those derived from published equations revealed that at high D/dp ratios the measured and calculated velocity profiles behaved similarly. At low ratios, oscillations in the velocity profiles agreed with those in the voidage profiles, signifying that treating the porous medium as a continuum medium is questionable in these cases.

Dynamics of follicle populations and gonadotropin concentrations in fillies age two to ten months

Follicle populations and concentrations of circulating gonadotropins were studied during age 2-10 months in 10 spring-born pony fillies. Blood sampling and ultrasound scanning were done every 4 days and daily for four 30 day periods. During 5-12 weeks, FSH concentrations were lower in 6 fillies with follicles greater than or equal to 6 mm (mean +/- s.e. 1.4 +/- 0.1 ng/ml) than in 4 fillies with follicles <6 mm (2.8 + 0.3 ng/ml). The diameters and numbers of follicles and gonadotropin concentrations increased progressively during age 2-4 months. A plateau in follicle activity and reduced levels of gonadotropins occurred during 5-7 months. During 8-10 months, follicles grew to >10 mm and gonadotropin concentrations increased. Waves of follicular growth were identified during the 30 day periods by significant increases in the diameter of the 10 largest follicles. The waves did not partition into dominant and subordinate follicles. Results indicated an initial postnatal period of negative ovarian feedback, temporally related changes in gonadotropins and follicles for months 3-10, and development of follicles in waves.

DYNAMICS OF COLONIZATION AND GYNE PRODUCTION BY MONOMORIUM-PHARAONIS (L) (HYM, FORMICIDAE) IN BRAZIL

The colonization characteristics of two neighboring populations of Monomorium pharaonis in human structures in Brazil were compared. No differences in the seasonality of colonizations into fixed trap nests between the two populations were found. However, one population had higher frequencies of colonizations with accompanying queens than the other. This resulted in the other population producing new queens at a higher frequency than the other. There was a clumping of colonization attempts at specific points, which shows that colonization may be predictable. These findings may be of importance in control programs for M. pharaonis in structures.

Ashcroft model potential study of lattice dynamics of α-iron and barium

Ashcroft model potential has been used to compute phonon dispersion relations along the three principal symmetry directions, i.e. [k00], [kk0] and [kkk] for alpha-iron and barium. The computed phonons gave a reasonable agreement with the experimental ones in all the three principal summetry directions expect for the T-2 branch in [KK0] direction where the present study failed to reproduce the experimental findings.

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.

DISTRIBUTION AND SEASONAL DYNAMICS OF RHODOPHYTA IN THE PRETO RIVER BASIN, SOUTHEASTERN BRAZIL

Distribution and seasonal dynamics of freshwater Rhodophyta were investigated in the Preto River basin, located in northwestern São Paulo State, southeastern Brazil. Twenty-two sites were sampled, six monthly during one year, four bimonthly during two years, and 12 twice (hot-rainy and cool-dry seasons) during the study period (May 1989 through March 1991). Red algal representatives were found in 19 sites (86.4%). Four species occurred in the basin with varying frequencies: Batrachospermum delicatulum (54.5%), Compsopogon coeruleus (36.4%), B. bicudoi (13.6%) and B. virgatum (4.5%). In addition, 'Chantransia' stage of the batrachospermalean species was found in 17 sites (77.3%). B. bicudoi, B. virgatum and C. coeruleus occurred only in large stream segments (greater-than-or-equal-to 3-order), generally in the main river, whereas B. delicatulum was more frequent in small streams (less-than-or-equal-to 3-order). The stream variables most closely related to the species distribution in the basin were specific conductance, pH and oxygen. B. bicudoi and B. delicatulum showed a marked seasonality: gametophytes were observed from late fall to early spring, while the 'Chantransia' stage generally occurred throughout the year. C. coeruleus was observed throughout the year in most sites, but the populations were generally more abundant from late fall to early spring. The combination of lower temperature and reduced turbidity resulting in increased illumination to the benthic algae during the dry winter months promotes the gametophytic growth of the batrachospermalean species, whereas current velocity was found to be the most influential stream variable for C. coeruleus. The persistance of the 'Chantransia' stage throughout the year as well as its tolerance to wider environmental conditions are key factors in the efficiency of the batrachospermalean life history strategy in lotic ecosystems.