Dynamics in dumbbell domains I. Continuity of the set of equilibria

We analyze the dynamics of a reaction-diffusion equation with homogeneous Neumann boundary conditions in a dumbbell domain. We provide an appropriate functional setting to treat this problem and, as a first step, we show in this paper the continuity of the set of equilibria and of its linear unstable manifolds. (c) 2006 Elsevier B.V. All rights reserved.

Dielectric and fatigue properties of Pb(Zr0.53Ti0.47)O-3 thin films prepared from oxide precursors method

Fatigue is an important problem to be considered if a ferroelectric film is used for non-volatile memory devices. In this phenomena, the remanent polarization and coercive field properties degrades in cycles which increase in hysteresis loops. The reasons have been attributed to different mechanisms such as a large voltage applied on ferroelectric film in every reading process in Ferroelectric Random Access Memory (FeRAM) or memories for digital storage in computer, grain size effects and others. The aim of this work is to investigate the influence of the crystallization kinetics on dielectric and ferroelectric properties of the Pb(Zr0.53Ti0.47)O-3 thin films prepared by an alternative chemical method. Films were crystallized in air on Pt/Ti/SiO2/Si substrates at 700 degrees C for 1 hour, in conventional thermal annealing (CTA), and at 700 degrees C for 1 min and 700 degrees C 5 min, using a rapid thermal annealing (RTA) process. Final films were crack free and presented an average of 750 nm in thickness. Dielectric properties were studied in the frequency range of 100 Hz - 1 MHz. All films showed a dielectric dispersion at low frequency. Ferroelectric properties were measured from hysteresis loops at 10 kHz. The obtained remanent polarization (P-r) and coercive field (E-c) were 3.7 mu C/cm(2) and 71.9 kV/cm respectively for film crystallized by CTA while in films crystallized by RTA these parameters were essentially the same. In the fatigue process, the P, value decreased to 14% from the initial value after 1.3 x 10(9) switching cycles, for film by CTA, while for film crystallized by RTA for 5 min, P, decreased to 47% from initial value after 1.7 x 10(9) switching cycles.

A Transmission Problem for Euler-Bernoulli beam with Kelvin-Voigt Damping

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Centers on center manifolds in the Lu system

We confirm a conjecture of Mello and Coelho [Phys. Lett. A 373 (2009) 1116] concerning the existence of centers on local center manifolds at equilibria of the Lu system of differential equations on R(3). Our proof shows that the local center manifolds are algebraic ruled surfaces, and are unique. (C) 2011 Elsevier B.V. All rights reserved.

Dynamics in dumbbell domains III. Continuity of attractors

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Two-body Dirac equation approach to the deuteron

The two-body Dirac(Breit) equation with potentials associated to one-boson-exchanges with cutoff masses is solved for the deuteron and its observables calculated. The 16-component wave-function for the Jπ = 1+ state contains four independent radial functions which satisfy a system of four coupled differential equations of first order. This system is numerically integrated, from infinity towards the origin, by fixing the value of the deuteron binding energy and imposing appropriate boundary conditions at infinity. For the exchange potential of the pion, a mixture of direct plus derivative couplings to the nucleon is considered. We varied the pion-nucleon coupling constant, and the best results of our calculations agree with the lower values recently determined for this constant.

Improved numerical approach for the time-independent Gross-Pitaevskii nonlinear Schrödinger equation

In the present work, we improve a numerical method, developed to solve the Gross-Pitaevkii nonlinear Schrödinger equation. A particular scaling is used in the equation, which permits us to evaluate the wave-function normalization after the numerical solution. We have a two-point boundary value problem, where the second point is taken at infinity. The differential equation is solved using the shooting method and Runge-Kutta integration method, requiring that the asymptotic constants, for the function and its derivative, be equal for large distances. In order to obtain fast convergence, the secant method is used. © 1999 The American Physical Society.

Behavioural Analysis of a Nonlinear Mechanical System Using Transient Trajectories

This work aims at a better comprehension of the features of the solution surface of a dynamical system presenting a numerical procedure based on transient trajectories. For a given set of initial conditions an analysis is made, similar to that of a return map, looking for the new configuration of this set in the first Poincaré sections. The mentioned set of I.C. will result in a curve that can be fitted by a polynomial, i.e. an analytical expression that will be called initial function in the undamped case and transient function in the damped situation. Thus, it is possible to identify using analytical methods the main stable regions of the phase portrait without a long computational time, making easier a global comprehension of the nonlinear dynamics and the corresponding stability analysis of its solutions. This strategy allows foreseeing the dynamic behavior of the system close to the region of fundamental resonance, providing a better visualization of the structure of its phase portrait. The application chosen to present this methodology is a mechanical pendulum driven through a crankshaft that moves horizontally its suspension point.

Consequences of quadratic frictional force on the one dimensional bouncing ball model

Some dynamical properties of the one dimensional Fermi accelerator model, under the presence of frictional force are studied. The frictional force is assumed as being proportional to the square particle's velocity. The problem is described by use of a two dimensional non linear mapping, therefore obtained via the solution of differential equations. We confirm that the model experiences contraction of the phase space area and in special, we characterized the behavior of the particle approaching an attracting fixed point. © 2007 American Institute of Physics.

On the Chaotic Suppression of Both Ideal and Non-ideal Duffing Based Vibrating Systems, Using a Magnetorheological Damper

In this paper the dynamics of the ideal and non-ideal Duffing oscillator with chaotic behavior is considered. In order to suppress the chaotic behavior and to control the system, a control signal is introduced in the system dynamics. The control strategy involves the application of two control signals, a nonlinear feedforward control to maintain the controlled system in a periodic orbit, obtained by the harmonic balance method, and a state feedback control, obtained by the state dependent Riccati equation, to bring the system trajectory into the desired periodic orbit. Additionally, the control strategy includes an active magnetorheological damper to actuate on the system. The control force of the damper is a function of the electric current applied in the coil of the damper, that is based on the force given by the controller and on the velocity of the damper piston displacement. Numerical simulations demonstrate the effectiveness of the control strategy in leading the system from any initial condition to a desired orbit, and considering the mathematical model of the damper (MR), it was possible to control the force of the shock absorber (MR), by controlling the applied electric current in the coils of the damper. © 2012 Foundation for Scientific Research and Technological Innovation.

A semigroups theory approach to a model of suspension bridges

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

Soluções auto-similares das equações de Navier-Stokes em Lp-Fraco

Pós-graduação em Matemática - IBILCE

Estudo analítico/numérico do problema de ablação em corpos rombudos com simetria axial

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estrutura hamiltoniana da hierarquia PIV

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Modelos matemáticos e aplicações ao ensino médio

Pós-graduação em Matemática em Rede Nacional - IBILCE