Symmetric Periodic Solutions of the Anisotropic Manev Problem

We consider the Manev Potential in an anisotropic space, i.e., such that the force acts differently in each direction. Using a generalization of the Poincare' continuation method we study the existence of periodic solutions for weak anisotropy. In particular we find that the symmetric periodic orbits of the Manev system are perturbed to periodic orbits in the anisotropic problem.Comment: Late

Rosette Central Configurations, Degenerate central configurations and bifurcations

In this paper we find a class of new degenerate central configurations and bifurcations in the Newtonian $n$-body problem. In particular we analyze the Rosette central configurations, namely a coplanar configuration where $n$ particles of mass $m_1$ lie at the vertices of a regular $n$-gon, $n$ particles of mass $m_2$ lie at the vertices of another $n$-gon concentric with the first, but rotated of an angle $\pi/n$, and an additional particle of mass $m_0$ lies at the center of mass of the system. This system admits two mass parameters $\mu=m_0/m_1$ and \ep=m_2/m_1. We show that, as $\mu$ varies, if $n> 3$, there is a degenerate central configuration and a bifurcation for every \ep>0, while if $n=3$ there is a bifurcations only for some values of $\epsilon$.Comment: 16 pages, 6 figure

Seven-body central configurations: a family of central configurations in the spatial seven-body problem

The main result of this paper is the existence of a new family of central configurations in the Newtonian spatial seven-body problem. This family is unusual in that it is a simplex stacked central configuration, i.e the bodies are arranged as concentric three and two dimensional simplexes.Comment: 15 pages 5 figure

Relative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities

We examine in detail the relative equilibria in the four-vortex problem where two pairs of vortices have equal strength, that is, \Gamma_1 = \Gamma_2 = 1 and \Gamma_3 = \Gamma_4 = m where m is a nonzero real parameter. One main result is that for m > 0, the convex configurations all contain a line of symmetry, forming a rhombus or an isosceles trapezoid. The rhombus solutions exist for all m but the isosceles trapezoid case exists only when m is positive. In fact, there exist asymmetric convex configurations when m < 0. In contrast to the Newtonian four-body problem with two equal pairs of masses, where the symmetry of all convex central configurations is unproven, the equations in the vortex case are easier to handle, allowing for a complete classification of all solutions. Precise counts on the number and type of solutions (equivalence classes) for different values of m, as well as a description of some of the bifurcations that occur, are provided. Our techniques involve a combination of analysis and modern and computational algebraic geometry

The Kepler Problem with Anisotropic Perturbations

We study a 2-body problem given by the sum of the Newtonian potential and an anisotropic perturbation that is a homogeneous function of degree $-\beta$, $\beta\ge 2$. For $\beta>2$, the sets of initial conditions leading to collisions/ejections and the one leading to escapes/captures have positive measure. For $\beta>2$ and $\beta\ne 3$, the flow on the zero-energy manifold is chaotic. For $\beta=2$, a case we prove integrable, the infinity manifold of the zero-energy level is a disconnected set, which has heteroclinic connections with the collision manifold

Tight-binding study of the influence of the strain on the electronic properties of InAs/GaAs quantum dots

We present an atomistic investigation of the influence of strain on the electronic properties of quantum dots (QD's) within the empirical $s p^{3} s^{*}$ tight-binding (ETB) model with interactions up to 2nd nearest neighbors and spin-orbit coupling. Results for the model system of capped pyramid-shaped InAs QD's in GaAs, with supercells containing $10^{5}$ atoms are presented and compared with previous empirical pseudopotential results. The good agreement shows that ETB is a reliable alternative for an atomistic treatment. The strain is incorporated through the atomistic valence force field model. The ETB treatment allows for the effects of bond length and bond angle deviations from the ideal InAs and GaAs zincblende structure to be selectively removed from the electronic-structure calculation, giving quantitative information on the importance of strain effects on the bound state energies and on the physical origin of the spatial elongation of the wave functions. Effects of dot-dot coupling have also been examined to determine the relative weight of both strain field and wave function overlap.Comment: 22 pages, 7 figures, submitted to Phys. Rev. B (in press) In the latest version, added Figs. 3 and 4, modified Fig. 5, Tables I and II,.and added new reference

Multiband tight-binding theory of disordered ABC semiconductor quantum dots: Application to the optical properties of alloyed CdZnSe nanocrystals

Zero-dimensional nanocrystals, as obtained by chemical synthesis, offer a broad range of applications, as their spectrum and thus their excitation gap can be tailored by variation of their size. Additionally, nanocrystals of the type ABC can be realized by alloying of two pure compound semiconductor materials AC and BC, which allows for a continuous tuning of their absorption and emission spectrum with the concentration x. We use the single-particle energies and wave functions calculated from a multiband sp^3 empirical tight-binding model in combination with the configuration interaction scheme to calculate the optical properties of CdZnSe nanocrystals with a spherical shape. In contrast to common mean-field approaches like the virtual crystal approximation (VCA), we treat the disorder on a microscopic level by taking into account a finite number of realizations for each size and concentration. We then compare the results for the optical properties with recent experimental data and calculate the optical bowing coefficient for further sizes

Unique presentation of a giant mediastinal tumor as kyphosis: a case report

<p>Abstract</p> <p>Introduction</p> <p>Although posture distortion is a common problem in elderly patients, spinal deformity caused by a thymoma has not been previously reported. Thymomas are slowly growing tumors that predominantly cause respiratory symptoms.</p> <p>Case presentation</p> <p>We report the case of an 83-year-old woman who was admitted with a giant mediastinal mass that had caused progressive spinal distortion and weight loss to our department. The clinical and laboratory investigations that followed revealed one of the largest thymomas ever reported in the medical literature, presenting as a mass lesion placed at the left hemithorax. She underwent complete surgical excision of the tumor via a median sternotomy. Two years after the operation, she showed significant improvement in her posture, no pulmonary discomfort, and a gain of 20 kg; she remains disease free based on radiographic investigations.</p> <p>Conclusions</p> <p>In this case, a chronic asymmetric load on the spine resulted in an abnormal vertebral curvature deformity that presented as kyphosis.</p