Effects of the eccentricity on the primaries in the gravitational capture phenomenon

Gravitational capture is a characteristic of some dynamical systems in celestial mechanics, as in the elliptic restricted three-body problem that is considered in this paper. The basic idea is that a spacecraft (or any particle with negligible mass) can change a hyperbolic orbit with a small positive energy around a celestial body into an elliptic orbit with a small negative energy without the use of any propulsive system. The force responsible for this modification in the orbit of the spacecraft is the gravitational force of the third body involved in the dynamics. In this way, this force is used as a zero cost control, equivalent to a continuous thrust applied in the spacecraft. One of the most important applications of this property is the construction of trajectories to the Moon. The objective of the present paper is to study in some detail the effects of the eccentricity of the primaries in this maneuver.

On bifurcation and symmetry of solutions of symmetric nonlinear equations with odd-harmonic forcings

In this work we study existence, bifurcation, and symmetries of small solutions of the nonlinear equation Lx = N(x, p, epsilon) + mu f, which is supposed to be equivariant under the action of a group OHm, and where f is supposed to be OHm-invariant. We assume that L is a linear operator and N(., p, epsilon) is a nonlinear operator, both defined in a Banach space X, with values in a Banach space Z, and p, mu, and epsilon are small real parameters. Under certain conditions we show the existence of symmetric solutions and under additional conditions we prove that these are the only feasible solutions. Some examples of nonlinear ordinary and partial differential equations are analyzed. (C) 1995 Academic Press, Inc.

Bifurcation of limit cycles from a centre in R-4 in resonance 1:N

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

A new interpretation for the degradation phenomenon of ZnO varistors

The electrical degradation phenomena of zinc oxide-based varistors were studied using a high-energy current pulse and a.c. polarization at different temperatures. Activation energy measurements during the degradation process showed that these phenomena are associated with diffusion and that the diffusion-controlling species are slower than Zn., For degradation promoted by current pulses of 8×20 μs, the Schottky potential barrier deformation was measured. A decrease in height and width of the potential barrier due to the reduction of surface states density, N s, without a significant change in donor density, N d, was observed. To explain these results, a modification of the unstable components model is proposed for the potential barrier in which the degradation is due to oxi-reduction reactions between atomic defects. These reactions promote the elimination of zinc vacancies and/or adsorbed oxygen on the grain boundaries. © 1992 Chapman & Hall.

New phenomenon of nonlinear Regge trajectory and quantum dual string theory

The relation between the spin and the mass of an infinite number of particles in a q-deformed dual string theory is studied. For the deformation parameter q a root of unity, in addition to the relation of such values of q with the rational conformal field theory, the Fock space of each oscillator mode in the Fubini-Veneziano operator formulation becomes truncated. Thus, based on general physical grounds, the resulting spin-(mass)2 relation is expected to be below the usual linear trajectory. For such specific values of q, we find that the linear Regge trajectory turns into a square-root trajectory as the mass increases.

Modulational instability analysis of surface-waves in the Bénard-Marangoni phenomenon

By using the long-wave approximation, a system of coupled evolutions equations for the bulk velocity and the surface perturbations of a Bénard-Marangoni system is obtained. It includes nonlinearity, dispersion and dissipation, and it is interpreted as a dissipative generalization of the usual Boussinesq system of equations. Then, by considering that the Marangoni number is near the critical value M = -12, we show that the modulation of the Boussinesq waves is described by a perturbed Nonlinear Schrödinger Equation, and we study the conditions under which a Benjamin-Feir instability could eventually set in. The results give sufficient conditions for stability, but are inconclusive about the existence or not of a Benjamin-Feir instability in the long-wave limit. © 1995.

Interference phenomenon for the Faddeevian regularization of 2D chiral fermionic determinants

The classification of the regularization ambiguity of a 2D fermionic determinant in three different classes according to the number of second-class constraints, including the new Faddeevian regularization, is examined and extended. We find a new and important result that the Faddeevian class, with three second-class constraints, possesses a free continuous one parameter family of elements. The criterion of unitarity restricts the parameter to the same range found earlier by Jackiw and Rajaraman for the two-constraint class. We studied the restriction imposed by the interference of right-left modes of the chiral Schwinger model (χQED2) using Stone's soldering formalism. The interference effects between right and left movers, producing the massive vectorial photon, are shown to constrain the regularization parameter to belong to the four-constraint class which is the only nonambiguous class with a unique regularization parameter. ©1999 The American Physical Society.

The phenomenon of photoinhibition of photosynthesis and its importance in reforestation

Photoinhibition, defined as the inhibition of photosynthesis caused by excessive radiance, affects field production to a great extent. This phenomenon is particularly relevant in reforestation practices, when one deals with forests of rapid growth such as Eucalyptus. The imposition of additional stress factors during exposure to high radiance increases the potential for photoinhibitory effects, so the inhibition of photosynthesis indicates that the plant is submitted to stressful conditions. Photoinhibition can be reversible, playing a protective role for the photosynthetic systems, but it can also reflect damage that has already occurred in the photosynthetic apparatus, being irreversible in this case. In this review, we present the physiological and molecular mechanisms of photoinhibition and discuss the interaction between light and other stress factors and its effects on plants destined for reforestation. In addition, the present work analyzes some of the features and strategies that help plants avoid or restrict the occurrence of photoinhibition. For instance, pigments and enzymes which naturally occur in plants can prevent photoinhibition, while preadaptation to nonideal conditions can enhance tolerance to a certain stress factor. Most of these morphological, metabolic, and biochemical mechanisms of defense are related to the dissipation of excessive energy such as heat. Understanding these mechanisms can help improve cultivation procedures, avoid the plants' death, and increase productivity in the field.

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.

Emperipolesis in a Case of B-Cell Lymphoma: A Rare Phenomenon Outside of Rosai-Dorfman Disease

We describe a case of a diffuse large B-cell lymphoma with extensive emperipolesis phenomenon. Light microscopy revealed numerous CD68-positive/S-100-negative histiocytes containing viable neoplastic hematopoietic cells in their cytoplasm. Electron microscopy confirmed these findings. In this case, there was no evidence of Rosai-Dorfman disease either clinically or histologically. This report emphasizes that emperipolesis is not restricted to Rosai-Dorfman disease and can be found in other conditions including non-Hodgkin lymphomas. © 2003 Elsevier Inc. All rights reserved.

A note on non-degenerate umbilics and the path formulation for bifurcation problems

Path formulation can be used to classify and structure efficiently multiparameter bifurcation problems around fundamental singularities: the cores. The non-degenerate umbilic singularities are the generic cores for four situations in corank 2: the general or gradient problems and the ℤ 2-equivariant (general or gradient) problems. Those categories determine an interesting 'Russian doll' type of structure in the universal unfoldings of the umbilic singularities. One advantage of our approach is that we can handle one, two or more parameters using the same framework (even considering some special parameter structure, for instance, some internal hierarchy). We classify the generic bifurcations that occur in those cases with one or two parameters.