On the periodic solutions of a class of duffing differential equations

In this work we study the periodic solutions, their stability and bifurcation for the class of Duffing differential equation mathematical equation represented where C > 0, ε > 0 and Λ are real parameter, A(t), b(t) and h(t) are continuous T periodic functions and ε is sufficiently small. Our results are proved using the averaging method of first order.

Periodic orbits and non-integrability of Armbruster-Guckenheimer-Kim potential

In this paper we study the periodic orbits of the Hamiltonian system with the Armburster-Guckenheimer Kim potential and its C1 non-integrability in the sense of Liouville-Arnold.

Soluções quase periódicas para equações diferenciais funcionais

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Whitham method for the Benjamin-Ono-Burgers equation and dispersive shocks

The Whitham modulation equations for the parameters of a periodic solution are derived using the generalized Lagrangian approach for the case of the damped Benjamin-Ono equation. The structure of the dispersive shock is considered in this method.

Sistemas dinâmicos e equações diferenciais ordinárias

Pós-graduação em Matemática Universitária - IGCE

Estabilidade de pontos de equilíbrio e existência de soluções periódicas em alguns modelos bidimensionais

Pós-graduação em Matemática Universitária - IGCE

Soil Solution as Affected by Plant Residues and Nitrogen Rates

Cation mobility in acidic soils with low organic-matter contents depends not only on sorption intensity but also on the solubility of the species present in soil solution. In general, the following leaching gradient is observed: potassium (K+) magnesium (Mg2+) calcium (Ca2+) aluminum (Al3+). To minimize nutrient losses and ameliorate the subsoil, soil solution must be changed, favoring higher mobility of M2+ (metal ions) forms. This would be theoretically possible if plant residues were kept on the soil surface. An experiment was conducted in pots containing a Distroferric Red Latosol, with soil solution extractors installed at two depths. Pearl millet, black oat, and oilseed radish residues were laid on the soil surface, and nitrogen (as ammonium nitrate) was applied at rates ranging from 0 to 150mgkg-1. Corn was grown for 52 days. Except for K+ and ammonium (NH4 +), nitrogen rates and plant residues had little effect upon the concentrations and forms of the elements in the soil solution. Presence of cover crop residues on soil surface decreased the effect of nitrogen fertilizer on Ca leaching. More than 90% of the Ca2+, Mg2+, and K+ were found as free ions. The Al3+ was almost totally complexed as Al(OH3)0. Nitrogen application increased the concentrations of almost all the ions in soil solution, including Al3+, although there was no modification in the leaching gradient.

Time-periodic perturbation of a Lienard equation with an unbounded homoclinic loop

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Periodic perturbations of quadratic planar polynomial vector fields

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Resonance in Bose-Einstein condensate oscillation from a periodic variation in scattering length

Using the explicit numerical solution of the axially symmetric Gross-Pitaevskii equation, we study the oscillation of the Bose-Einstein condensate (BEC) induced by a periodic variation in the atomic scattering length a. When the frequency of oscillation of a is an even multiple of the radial or axial trap frequency, respectively, the radial or axial oscillation of the condensate exhibits resonance with a novel feature. In this nonlinear problem without damping, at resonance in the steady state the amplitude of oscillation passes through a maximum and minimum. Such a growth and decay cycle of the amplitude may keep on repeating. Similar behaviour is also observed in a rotating BEC.

A note about the appearance of non-hyperbolic solutions in a mechanical pendulum system

The investigation of the behavior of a nonlinear system consists in the analysis of different stages of its motion, where the complexity varies with the proximity of a resonance region. Near this region the stability domain of the system undergoes sudden changes due basically to competition and interaction between periodic and saddle solutions inside the phase portrait, leading to the occurrence of the most different phenomena. Depending of the domain of the chosen control parameter, these events can reveal interesting geometric features of the system so that the phase portrait is not capable to express all them, since the projection of these solutions on the two-dimensional surface can hide some aspects of these events. In this work we will investigate the numerical solutions of a particular pendulum system close to a secondary resonance region, where we vary the control parameter in a restrict domain in order to draw a preliminary identification about what happens with this system. This domain includes the appearance of non-hyperbolic solutions where the basin of attraction in the center of the phase portrait diminishes considerably, almost disappearing, and afterwards its size increases with the direction of motion inverted. This phenomenon delimits a boundary between low and high frequency of the external excitation.

Comments on energy confinement in non-periodic structures

In this study, we investigate the possibility of mode localization occurrence in a non-periodic Pfluger's column model of a rocket with an intermediate concentrated mass at its middle point. We discuss the effects of varying the intermediate mass magnitude and its position and the resulting energy confinement for two cases. Free vibration analysis and the severity of mode localization are appraised, without decoupling the system, by considering as a solution basis the fundamental free response or dynamical solution. This allows for the reduction of the dimension of the algebraic modal equation that arises from satisfying the boundary and continuity conditions. By using the same methodology, we also consider the case of a cantilevered Pluger's column with rotational stiffness at the middle support instead of an intermediate concentrated mass. (c) 2008 Elsevier Ltd. All rights reserved.

Solid-state and solution structural study of acetylacetone-modified tin(IV) chloride used as a precursor of SnO2 nanoparticles prepared by a sol-gel route

The effect of addition of different amounts of acetylacetone (acacH) on the species formed at room temperature and after thermohydrolysis at 70 degreesC for 30 and 120 min of ethanolic SnCl4.5H(2)O solutions is followed by EXAFS spectroscopy at the Sn K-edge. We show that thermohydrolyzed solutions are a mixture of SnO2 nanoparticles and soluble tin polynuclear species. The complexation of the tin molecular precursors by acetylacetonate ligands is evidenced by H-1, C-13, and Sn-119 NMR spectroscopy and EXAFS for a acacH/Sn ratio higher than 2. Single crystals are isolated from solution and the structure, determined by X-ray diffraction, is built up from monomeric Cl-3(H2O)Sn(acac)-H2O units bridged together by hydrogen bonding. The acacH/Sn ratio in solution controls the polycondensation of the hydrolyzed species but not the crystallite size of the SnO2 nanoparticles (similar to2 nm). Because of the major presence of chelated tin mono- and dimeric complexes in solution for acacH/Sn > 2, the condensation is almost inhibited, meanwhile the decrease of amount of chelated complexes for the acacH/Sn < 2 gives rise to an increase of the number of nanoparticles.

Magnesium levels in nutrient solution and common bean (Phaseolus vulgaris L cv Carioca) development. Evaluation of the growth relations and assimilate partitioning

The effect of magnesium levels in nutrient solution upon relation between shoot and root, leaf weight ratio and assimilate partitioning of common bean (Phaseolus vulgaris L. cv Carioca) was studied. Bean plants (3 per pot) were grown in 6 l pots containing Hoagland & Arnon n. 2 solution modified to obtain 2.4, 24.3, 48.6, 72.9 and 97.2 ppm of magnesium. The experimental design was a completely randomized factorial replicated 3 times with 5 levels of magnesium and 5 samplings wich were done forthnightly. Therefore, it may be suggested that the 48.6 ppm of magnesium level proposed by Hoagland & Amen (1950) is the best choice for the common bean, according to the conditions of this experiment. Magnesium concentrations over 48.6 ppm didn't show significant alterations of the evaluated parameters. Nutrient solution with 2.4 ppm of magnesium content provides higher efficiency to the common bean plants during almost all its cycle, except the final of the reproductive phase. These results suggest that magnesium concentration increased to 48.6 ppm, in the cycle final perhaps could increase the productivity.

Pb1-xCaxTiO3 solid solution (x=0.0, 0.25, 0.50, and 0.75): A theoretical and experimental approach

In this paper we report an experimental and theoretical study based on a periodic density functional investigation into selected compositions of Pb1-xCaxTiO3 (x=0.0, 0.25, 0.50, and 0.75). Based on our findings, we propose that the pseudocubic structure of these perovskites presents a long-range tendency for cubic symmetry, while the short-range displacements bring the solid solution to a tetragonal symmetry. The results are discussed in terms of x-ray diffraction, structural optimized parameters, Raman spectroscopy, band structure, density of states, Mulliken charge, and overlap population.