Numerical exploration of resonant dynamics in the system of Saturnian major satellites

We numerically investigate the long-term dynamics of the Saturnian system by analyzing the Fourier spectra of ensembles of orbits taken around the current orbits of Mimas, Enceladus, Tethys, Rhea and Hyperion. We construct dynamical maps around the current position of these satellites in their respective phase spaces. The maps are the result of a great deal of numerical simulations where we adopt dense sets of initial conditions and different satellite configurations. Several structures associated to the current two-body mean-motion resonances, unstable regions associated to close approaches between the satellites, and three-body mean-motion resonances in the system, are identified in the map. (C) 2010 Elsevier Ltd. All rights reserved.

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.

Nonlinear Dynamics and Control of an Ideal/Nonideal Load Transportation System With Periodic Coefficients

In this paper, a loads transportation system in platforms or suspended by cables is considered. It is a monorail device and is modeled as an inverted pendulum built on a car driven by a dc motor the governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the dc motor and the dynamical system, that is, we have a so called nonideal periodic problem. The problem is analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, we also analyze the problem quantitatively using the Floquet multipliers technique. Finally, we devise a control for the studied nonideal problem. The method that was used for analysis and control of this nonideal periodic system is based on the Chebyshev polynomial exponsion, the Picard iterative method, and the Lyapunov-Floquet transformation (L-F transformation). We call it Sinha's theory.

On the dynamics of the Bianchi IX system

In this paper, we study the flow on three invariant sets of dimension five for the classical Bianchi IX system. In these invariant sets, using the Darboux theory of integrability, we prove the non-existence of periodic solutions and we study their dynamics. Moreover, we find three invariant sets of dimension four where the flow is integrable.

Dynamics and coexistence in a system with intraguild mutualism

It is a tenet of ecological theory that two competing consumers cannot stably coexist on a single limiting resource in a homogeneous environment. Many mechanisms and processes have since been evoked and studied, empirically and theoretically, to explain species coexistence and the observed biological diversity. Facilitative interactions clearly have the potential to enhance coexistence. Yet, even though mutual facilitation between species of the same guild is widely documented empirically, the subject has received very little theoretical attention. Here, we study one form of intraguild mutualism in the simplest possibly community module of one resource and two consumers. We incorporate mutualism as enhanced consumption in the presence of the other consumers. We find that intraguild mutualism can (a) significantly enhance coexistence of consumers, (b) induce cyclic dynamics, and (c) give rise to a bi-stability (a 'joint' Allee effect) and potentially catastrophic collapse of both consumer species. © 2012 Elsevier B.V.

Dynamics of cell and tissue genesis in the male reproductive system of ticks (Acari: Ixodidae) Amblyomma cajennese (Fabricius, 1787) and Amblyomma aureolatum (Pallas, 1772): a comparative analysis

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

Influence of ideal and non-ideal excitation sources on the dynamics of a nonlinear vibro-impact system

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

Zero, minimum and maximum relative radial acceleration for planar formation flight dynamics near triangular libration points in the Earth-Moon system

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

Nonlinear dynamics and control strategies: On a energy harvester vibrating system with a linear form to non-ideal motor torque

In this paper, we deal with the research of a vibrating model of an energy harvester device, including the nonlinearities in the model of the piezoelectric coupling and the non-ideal excitation. We show, using numerical simulations, in the analysis of the dynamic responses, that the harvested power is influenced by non-linear vibrations of the structure. Chaotic behavior was also observed, causing of the loss of energy throughout the simulation time. Using a perturbation technique, we find an approximate analytical solution for the non-ideal system. Then, we apply both two control techniques, to keep the considered system, into a stable condition. Both the State Dependent Ricatti Equation (SDRE) control as the feedback control by changing the energy of the oscillator, were efficient in controlling of the considered non-ideal system.

Chaotic Dynamics in a Low-Energy Transfer Strategy to the Equilateral Equilibrium Points in the Earth-Moon System

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

How population loss through habitat boundaries determines the dynamics of a predator-prey system

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

On nonlinear dynamics behavior and control of a new model of a magnetically levitated vibrating system, excited by an unbalanced DC motor of limited power supply

We analyze new results on a magnetically levitated body (a block including a magnet whose bottom pole is set in such a way as to repel the upper pole of a magnetic base) excited by a non-ideal energy source (an unbalanced electric motor of limited power supply). These new results are related to the jump phenomena and increase of power required of such sources near resonance are manifestations of a non-ideal system and they are referred as the Sommerfeld effect, which emulates an energy sink. In this work, we also discuss control strategies to be applied to this system, in resonance conditions, in order to decrease its vibration amplitude and avoiding this apparent energy sink.

Organic material decomposition and nutrient dynamics in a mulch system enriched with leguminous trees in the Amazon

As novas técnicas propostas para a agricultura na Amazônia incluem sistema de rotação de capoeira enriquecido com árvores leguminosas e transformando a queima da biomassa em cobertura morta sobre o solo. A decomposição e a liberação de nutrientes da cobertura morta foram estudadas usando sacos de liteira com malha fina que continham cinco tratamentos com diferentes espécies de leguminosas em comparação a um tratamento-controle com vegetação natural. As amostras para cada tratamento foram analisadas para conteúdos de C total, N, P, K, Ca, Mg, lignina, celulose e polifenóis solúveis em diferentes tempos de amostragem durante um ano. A razão constante de decomposição variou com a espécie e com o tempo. A perda de massa nos sacos de decomposição foi de 30,1 % para Acacia angustissima, de 32,7 % para Sclerolobium paniculatum, de 33,9 % para Inga edulis e para a vegetação secundária, de 45,2 % para Acacia mangium e de 63,6 % para Clitoria racemosa. Foi observada imobilização de N e P em todos os tratamentos, sendo a mineralização do N negativamente correlacionada com o fenol, razão C/N, razão (lignina + fenol)/N, razão fenol/P e o conteúdo de N nos sacos de liteira. Depois de 362 dias de incubação no campo, 3,3 % de K, 32,2 % de Ca e 22,4 % de Mg permaneceram no material em decomposição. Os resultados evidenciaram que a baixa qualidade mineral e a alta quantidade de carbono orgânico e aplicado como cobertura morta podem limitar a quantidade de energia disponível para os microrganismos resultando em uma competição por nutrientes com as plantas agrícolas.

Dynamics of cell and tissue genesis in the male reproductive system of ticks (Acari: Ixodidae) Amblyomma cajennense (Fabricius, 1787) and Amblyomma aureolatum (Pallas, 1772): a comparative analysis

Ticks are classified into three families: Argasidae, Ixodidae, and Nutalliellidae. The taxonomy and phylogeny within Ixodidae are still discussed by the specialists, thus requiring further studies. Amblyomma cajennese and Amblyomma aureolatum (Brazil) belong to two species complexes known as “cajennese” and “ovale”, respectively, and are directly related to the transmission of the Brazilian spotted fever. This confirms the medical and veterinary significance of these species, as well as the need for further morphological studies that will bring a better understanding of their taxonomy, phylogeny, and control. In this context, the present study aimed to characterize the morphology of the male reproductive system of A. cajennese and A. aureolatum when unfed and after 4 days of feeding, thereby seeking to: (a) distinguish the two species or “complexes”, and (b) study an internal system which has the potential to be targeted by acaricides. Therefore, males from both species (unfed and after 4 days of feeding) were cold-anesthetized, dissected, and had their reproductive systems removed for histological analysis. The results showed that the morphology of the male reproductive system is generally similar between both species, like in other Ixodidae ticks, exhibiting a multilobed accessory gland complex related to seminal fluid secretion, a pair of vasa deferentia and a pair of testes housing germ cells (spermatocytes) in different stages. The main differences were found in the development of the accessory gland complex cells and germ cells, showing that the maturation of the male reproductive system starts later in A. aureolatum, when compared to A. cajennese. However, during the blood meal, A. aureolatum development is increased, thus making germ cell maturation and gland complex activity higher than in A. cajennese. This study shows the differences in the development of the male reproductive systems of both species, while providing information that can assist in the establishment of new control methods.

Towards the construction of a validated numerical system to study the mesoscale dynamics of the North East Atlantic (2003-2006)

Máster en Oceanografía