The stability evolution of a family of simply periodic lunar orbits

The present work deals with a family of simply periodic orbits around the Moon in the rotating Earth Moon-particle system. Taking the framework of the planar, circular, restricted three-body problem, we follow the evolution of this family of periodic orbits using the numerical technique of Poincaré surface of section. The maximum amplitude of oscillation about the periodic orbits are determined and can be used as a parameter to measure the degree of stability in the phase space for such orbits. Despite the fact that the whole family of periodic orbits remain stable, there is a dichotomy in the quasi-periodic ones at the Jacobi constant Cj = 2.85. The quasi-periodic orbits with Cj < 2.85 oscillate around the periodic orbits in a different way from those with Cj > 2.85. © 1999 Elsevier Science Ltd. All rights reserved.

Solutions for a class of integro-differential equations with time periodic coefficients

In this work, a series solution is found for the integro-differential equation y″ (t) = -(ω2 c + ω2 f sin2 ωpt)y(t) + ωf (sin ωpt) z′ (0) + ω2 fωp sin ωpt ∫t 0 (cos ωps) y(s)ds, which describes the charged particle motion for certain configurations of oscillating magnetic fields. As an interesting feature, the terms of the solution are related to distinct sequences of prime numbers.

Array of Bose-Einstein condensates under time-periodic Feshbach-resonance management

The investigation of the dynamics of a discrete soliton in an array of Bose-Einstein condensates under the action of a periodically time-modulated atomic scattering length [Feshbach-resonance management (FRM)] was discussed. The slow and rapid modulations, in comparison with the tunneling frequency were considered. An averaged equation, which was a generalized discrete nonlinear Schrödinger equation, including higher-order effective nonlinearities and intersite nonlinear interactions was derived in the case of the rapid modulation. It was demonstrated that the modulations of sufficient strength results in splitting of the soliton by direct simulations.

An overview of the microstructures present in high-speed steel - Carbides crystallography

The aim of the work was to prepare an overview about the microstructures present in high-speed steel, focused on the crystallography of the carbides. High-speed steels are currently obtained by casting, powder metallurgy and more recently spray forming. High-speed steels have a high hardness resulting from a microstructure, which consists of a steel matrix (martensite and ferrite), in which embedded carbides of different crystal structure, chemical composition, morphology and size, exist. These carbides are commonly named MxC, where M represents one or more metallic atoms. These carbides can be identified by X-ray diffraction considering M as a unique metallic atom. In this work, it is discussed, in basis of the first principles of physics crystallography, the validation of this identification when it is considered that other atoms in the structure are substitutional. Further, it is discussed some requirements for data acquisition that allows the Rietveld refinement to be applied on carbide crystallography and phase amount determination.

On the existence and stability of periodic orbits in non ideal problems: General results

In this work, motivated by non-ideal mechanical systems, we investigate the following O.D.E. ẋ = f (x) + εg (x, t) + ε2g (x, t, ε), where x ∈ Ω ⊂ ℝn, g, g are T periodic functions of t and there is a 0 ∈ Ω such that f (a 0) = 0 and f′ (a0) is a nilpotent matrix. When n = 3 and f (x) = (0, q (x 3) , 0) we get results on existence and stability of periodic orbits. We apply these results in a non ideal mechanical system: the Centrifugal Vibrator. We make a stability analysis of this dynamical system and get a characterization of the Sommerfeld Effect as a bifurcation of periodic orbits. © 2007 Birkhäuser Verlag, Basel.

On the photonic dispersion of periodic superlattices made of left-handed materials

Studies of the band gap properties of one-dimensional superlattices with alternate layers of air and left-handed materials are carried out within the framework of Maxwell's equations. By left-handed material, we mean a material with dispersive negative electric and magnetic responses. Modeling them by Drude-type responses or by fabricated ones, we characterize the n(ω) = 0 gap, i.e., the zeroth order gap, which has been predicted and detected. The band structure and analytic equations for the band edges have been obtained in the long wavelength limit in case of periodic, Fibonacci, and Thue-Morse superlattices. Our studies reveal the nature of the width of the zeroth order band gap, whose edge equations are defined by null averages of the response functions. Oblique incidence is also investigated, yielding remarkable results. © 2010 Springer Science+Business Media B.V.

Optimal low-cost transfer to L4 and L5 lagrangian points based on G-family of periodic orbits

An alternative transfer strategy to send spacecrafts to stable orbits around the Lagrangian equilibrium points L4 and L5 based in trajectories derived from the periodic orbits around LI is presented in this work. The trajectories derived, called Trajectories G, are described and studied in terms of the initial generation requirements and their energy variations relative to the Earth through the passage by the lunar sphere of influence. Missions for insertion of spacecrafts in elliptic orbits around L4 and L5 are analysed considering the Restricted Three-Body Problem Earth- Moon-particle and the results are discussed starting from the thrust, time of flight and energy variation relative to the Earth. Copyright© (2012) by the International Astronautical Federation.

Anisotropy in the transport properties of type II superconducting films with periodic pinning

Using numerical simulations, we analyze the anisotropy effects in the critical currents and dynamical properties of vortices in a thin superconducting film submitted to hexagonal and Kagomé periodical pinning arrays. The calculations are performed at zero temperature, for transport currents parallel and perpendicular to the main axis of the lattice, and parallel to the diagonal axis of the rhombic unit cell. We show that the critical currents and dynamic properties are anisotropic for both pinning arrays and all directions of the transport current. The anisotropic effects are more significant just above the critical current and disappear with higher values of current and both pinning arrays. The dynamical phases for each case and a wide range of transport forces are analyzed. © 2012 Springer Science+Business Media, LLC.

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.

Hydrostatic and [001] uniaxial pressure on anatase TiO2 by periodic B3LYP-D* calculations

The effect of high hydrostatic and [001] uniaxial pressures on TiO 2 anatase was studied under the framework of periodic calculations with the inclusion of DFT-D2 dispersion potential adjusted for this system (B3LYP-D*). The role of dispersion in distorted unit cells was evaluated in terms of lattice parameters, elastic constants, equation of state, vibrational properties, and electronic properties (band structure and density of states). A more reliable description at high pressures was achieved because the B3LYP-D* presented an improvement in all properties for undistorted bulk over conventional B3LYP and B3LYP-D. From density of states analysis, we observed that the contribution of crystalline orbitals to the edge of valence and conduction bands changed within applied pressure. The studied distortions can give some insight into behavior of electronic and structural properties due to local stress in anatase bulk from doping, defects, and physical tensions in nanometric forms. © 2013 American Chemical Society.

Critical currents and melting temperature of a two-dimensional vortex lattice with periodic pinning

The critical current and melting temperature of a vortex system are analyzed. Calculations are made for a two-dimensional film at finite temperature with two kinds of periodic pinning: hexagonal and Kagomé. A transport current parallel and perpendicular to the main axis of the pinning arrays is applied and molecular dynamics simulations are used to calculate the vortex velocities to obtain the critical currents. The structure factor and displacements of vortices at zero transport current are used to obtain the melting temperature for both pinning arrays. The critical currents are higher for the hexagonal pinning lattice and anisotropic for both pinning arrays. This anisotropy is stronger with temperature for the hexagonal array. For the Kagomé pinning lattice, our analysis shows a multi stage phase melting; that is, as we increase the temperature, each different dynamic phase melts before reaching the melting temperature. Both the melting temperature and critical currents are larger for the hexagonal lattice, indicating the role for the interstitial vortices in decreasing the pinning strength. © 2012 Springer Science+Business Media New York.

Periodic compression of an adiabatic gas: Intermittency-enhanced Fermi acceleration

A gas of non-interacting particles diffuses in a lattice of pulsating scatterers. In the finite-horizon case with bounded distance between collisions and strongly chaotic dynamics, the velocity growth (Fermi acceleration) is well described by a master equation, leading to an asymptotic universal non-Maxwellian velocity distribution scaling as v∼t. The infinite-horizon case has intermittent dynamics which enhances the acceleration, leading to v∼t ln t and a non-universal distribution. © Copyright EPLA, 2013.

Periodic solutions for nonlinear telegraph equationvia elliptic regularization

ABSTRACT: In this work we are concerned with the existence and uniqueness of T -periodic weak solutions for an initial-boundary value problem associated with nonlinear telegraph equations typein a domain. Our arguments rely on elliptic regularization technics, tools from classical functional analysis as well as basic results from theory of monotone operators.

Preparation of TiO2/SnO2 Thin Films by Sol-Gel Method and Periodic B3LYP Simulations

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

Periodic solutions of el nino model through the vallis differential system

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)