Periodic orbits near a heteroclinic loop formed by one dimensional orbit and a 2-dimensional manifold: application to the charged collinear 3-body problem

The paper is devoted to the study of a type of differential systems which appear usually in the study of some Hamiltonian systems with 2 degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear 3–body problem.

Raman microstructural analysis of silicon-on-insulator formed by high dose oxygen ion implantation: As-implanted structures

A microstructural analysis of silicon-on-insulator samples obtained by high dose oxygen ion implantation was performed by Raman scattering. The samples analyzed were obtained under different conditions thus leading to different concentrations of defects in the top Si layer. The samples were implanted with the surface covered with SiO2 capping layers of different thicknesses. The spectra measured from the as-implanted samples were fitted to a correlation length model taking into account the possible presence of stress effects in the spectra. This allowed quantification of both disorder effects, which are determined by structural defects, and residual stress in the top Si layer before annealing. These data were correlated to the density of dislocations remaining in the layer after annealing. The analysis performed corroborates the existence of two mechanisms that generate defects in the top Si layer that are related to surface conditions during implantation and the proximity of the top Si/buried oxide layer interface to the surface before annealing.

Correlations between black holes formed in cosmic string breaking

An analysis of cosmic string breaking with the formation of black holes attached to the ends reveals a remarkable feature: the black holes can be correlated or uncorrelated. We find that, as a consequence, the number-of-states enhancement factor in the action governing the formation of uncorrelated black holes is twice the one for a correlated pair. We argue that when an uncorrelated pair forms at the ends of the string, the physics involved is more analogous to thermal nucleation than to particle-antiparticle creation. Also, we analyze the process of intercommuting strings induced by black hole annihilation and merging. Finally, we discuss the consequences for grand unified strings. The process whereby uncorrelated black holes are formed yields a rate which significantly improves over those previously considered, but still not enough to modify string cosmology. 1995 The American Physical Society.

Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2 in R3

In this paper we will find a continuous of periodic orbits passing near infinity for a class of polynomial vector fields in R3. We consider polynomial vector fields that are invariant under a symmetry with respect to a plane and that possess a “generalized heteroclinic loop” formed by two singular points e+ and e− at infinity and their invariant manifolds � and . � is an invariant manifold of dimension 1 formed by an orbit going from e− to e+, � is contained in R3 and is transversal to . is an invariant manifold of dimension 2 at infinity. In fact, is the 2–dimensional sphere at infinity in the Poincar´e compactification minus the singular points e+ and e−. The main tool for proving the existence of such periodic orbits is the construction of a Poincar´e map along the generalized heteroclinic loop together with the symmetry with respect to .

Symmetric periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds

In this paper we consider C1 vector fields X in R3 having a “generalized heteroclinic loop” L which is topologically homeomorphic to the union of a 2–dimensional sphere S2 and a diameter connecting the north with the south pole. The north pole is an attractor on S2 and a repeller on . The equator of the sphere is a periodic orbit unstable in the north hemisphere and stable in the south one. The full space is topologically homeomorphic to the closed ball having as boundary the sphere S2. We also assume that the flow of X is invariant under a topological straight line symmetry on the equator plane of the ball. For each n ∈ N, by means of a convenient Poincar´e map, we prove the existence of infinitely many symmetric periodic orbits of X near L that gives n turns around L in a period. We also exhibit a class of polynomial vector fields of degree 4 in R3 satisfying this dynamics.

Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

In this paper we consider vector fields in R3 that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e+ and e −) and their invariant manifolds: one of dimension 2 (a sphere minus the points e+ and e −) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e −). In particular, we analyze the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R3, and the second one is the charged rhomboidal four body problem.

Spectroscopic characterization of phases formed by high-dose carbon ion implantation in silicon

High-dose carbon-ion-implanted Si samples have been analyzed by infrared spectroscopy, Raman scattering, and x-ray photoelectron spectroscopy (XPS) correlated with transmission electron microscopy. Samples were implanted at room temperature and 500°C with doses between 1017 and 1018 C+/cm2. Some of the samples were implanted at room temperature with the surface covered by a capping oxide layer. Implanting at room temperature leads to the formation of a surface carbon-rich amorphous layer, in addition to the buried implanted layer. The dependence of this layer on the capping oxide suggests this layer to be determined by carbon migration toward the surface, rather than surface contamination. Implanting at 500°C, no carbon-rich surface layer is observed and the SiC buried layer is formed by crystalline ßSiC precipitates aligned with the Si matrix. The concentration of SiC in this region as measured by XPS is higher than for the room-temperature implantation.