Periodic waves and solitons of two-photon propagation

We study the two-photon propagation (TPP) modelling equations. The one-phase periodic solutions are obtained in an effective form. Their modulation is investigated by means of the Whitham method. The theory developed is applied to the problem of creation of TPP solitons on the sharp front of a long pulse.

Band-edge states of the zero(th)-order gap in quasi-periodic photonic superlattices

The photonic modes of Thue-Morse and Fibonacci lattices with generating layers A and B, of positive and negative indices of refraction, are calculated by the transfer-matrix technique. For Thue-Morse lattices, as well for periodic lattices with AB unit cell, the constructive interference of reflected waves, corresponding to the zero(th)-order gap, takes place when the optical paths in single layers A and B are commensurate. In contrast, for Fibonacci lattices of high order, the same phenomenon occurs when the ratio of those optical paths is close to the golden ratio. In the long wavelength limit, analytical expressions defining the edge frequencies of the zero(th) order gap are obtained for both quasi-periodic lattices. Furthermore, analytical expressions that define the gap edges around the zero(th) order gap are shown to correspond to the = 0 and = 0 conditions.

Application of impedance spectroscopy to evaluate the effect of different setting accelerators on the developed microstructures of calcium phosphate cements

The main goal of the present study was to evaluate the effect of different setting accelerator agents on the developed microstructures of calcium phosphate cements (CPCs) by employing the impedance spectroscopy (IS) technique. Six compositions of CPCs were prepared from mixtures of commercial dicalcium phosphate anhydrous (DCPA) and synthesized tetracalcium phosphate (TTCP) as the solid phases. Two TTCP/DCPA molar ratios (1/1 and 1/2) and three liquid phases (aqueous solutions of Na(2)HPO(4), tartaric acid (TA) and oxalic acid (OA), 5% volume fraction) were employed. Initial (I) and final (F) setting times of the cement pastes were determined with Gillmore needles (ASTM standard C266-99). The hardened samples were characterized by X-ray powder diffraction (XRD), Fourier transformed infrared (FTIR) spectroscopy, scanning electron microscopy (SEM), and apparent density measurements. The IS technique was employed as a non-destructive tool to obtain information related to porosity, tortuosity and homogeneity of the cement microstructures. The formulation prepared from a TTCP/DCPA equimolar mixture and OA as the liquid phase presented the shortest I and F (12 and 20 min, respectively) in comparison to the other studied systems. XRD analyses revealed the formation of low-crystallinity hydroxyapatite (HA) (as the main phase) as well as the presence of little amounts of unreacted DCPA and TTCP after 24 h hardening in 100% relative humidity. This was related to the proposed mechanisms of dissolution of the reactants. The bands observed by FTIR allowed identifying the presence of calcium tartrate and calcium oxalate in the samples prepared from TA and OA, in addition to the characteristic bands of HA. High degree of entanglement of the formed crystals was observed by SEM in samples containing OA. SEM images were also correlated to the apparent densities of the hardened cements. Changes in porosity, tortuosity and microstructural homogeneity were determined in all samples, from IS results, when the TTCP/DCPA ratio was changed from 1/1 to 1/2. The cement formulated from an equimolar mixture of TTCP/DCPA and OA as the liquid phase presented setting times, degree of conversion to low-crystallinity HA and microstructural features suitable to be used as potential bone cement in clinical applications. The IS technique was shown to be a very sensitive and non-destructive tool to relate the paste composition to the developed microstructures. This approach could be very useful to develop calcium phosphate bone cements for specific clinical demands.

Structural and Electronic Properties of Lithiated SnO2. A Periodic DFT Study

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Alternative Transfers to the NEOs 99942 Apophis, 1994 WR12, and 2007 UW1 via Derived Trajectories from Periodic Orbits of Family G

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

On the periodic solutions of the static, spherically symmetric Einstein-Yang-Mills equations

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

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.