Chaotic oscillation in an attractive Bose-Einstein condensate under an impulsive force

The chaotic oscillation in an attractive Bose-Einstein condensate (BEC) under an impulsive force was discussed using mean-field Gross-Pitaevskii (GP) equation. It was found that sustained chaotic oscillation resulted in a BEC under the action of an impulsive force generated by suddenly changing the interatomic scattering length or the harmonic oscillator trapping potential. The analysis suggested that the final state interatomic attraction played an important role in the generation of the chaotic dynamics.

Dynamic analysis of a new piezoelectric flextensional actuator using the J1-J4 optical interferometric method

Piezoelectric actuators are widely used in positioning systems which demand high resolution such as scanning microscopy, fast mirror scanners, vibration cancellation, cell manipulation, etc. In this work a piezoelectric flextensional actuator (PFA), designed with the topology optimization method, is experimentally characterized by the measurement of its nanometric displacements using a Michelson interferometer. Because this detection process is non-linear, adequate techniques must be applied to obtain a linear relationship between an output electrical signal and the induced optical phase shift. Ideally, the bias phase shift in the interferometer should remain constant, but in practice it suffers from fading. The J1-J4 spectral analysis method provides a linear and direct measurement of dynamic phase shift in a no-feedback and no-phase bias optical homodyne interferometer. PFA application such as micromanipulation in biotechnology demands fast and precise movements. So, in order to operate with arbitrary control signals the PFA must have frequency bandwidth of several kHz. However as the natural frequencies of the PFA are low, unwanted dynamics of the structure are often a problem, especially for scanning motion, but also if trajectories have to be followed with high velocities, because of the tracking error phenomenon. So the PFA must be designed in such a manner that the first mechanical resonance occurs far beyond this band. Thus it is important to know all the PFA resonance frequencies. In this work the linearity and frequency response of the PFA are evaluated up to 50 kHz using optical interferometry and the J1-J4 method.

Positronium-positronium interaction: resonance, scattering length, and Bose-Einstein condensation

The low-energy scattering of ortho positronium (Ps) by ortho Ps has been studied in a full quantum mechanical coupled-channel approach. In the singlet channel (total spin s(T) = 0) we find S- and P-wave resonances at 3.35 eV (width 0.02 eV) and 5.05 eV (width 0.04 eV), respectively, and a binding of 0.43 eV of Ps(2). The scattering length for s(T) = 0 is 3.95 Angstrom and for s(T) = 2 is 0.83 Angstrom. The small s(T) = 2 scattering length makes the spin-polarized ortho Ps atoms an almost noninteracting ideal gas which may undergo Bose-Einstein condensation. (C) 2002 Elsevier B.V. B.V. All rights reserved.

A note about the appearance of non-hyperbolic solutions in a mechanical pendulum system

The investigation of the behavior of a nonlinear system consists in the analysis of different stages of its motion, where the complexity varies with the proximity of a resonance region. Near this region the stability domain of the system undergoes sudden changes due basically to competition and interaction between periodic and saddle solutions inside the phase portrait, leading to the occurrence of the most different phenomena. Depending of the domain of the chosen control parameter, these events can reveal interesting geometric features of the system so that the phase portrait is not capable to express all them, since the projection of these solutions on the two-dimensional surface can hide some aspects of these events. In this work we will investigate the numerical solutions of a particular pendulum system close to a secondary resonance region, where we vary the control parameter in a restrict domain in order to draw a preliminary identification about what happens with this system. This domain includes the appearance of non-hyperbolic solutions where the basin of attraction in the center of the phase portrait diminishes considerably, almost disappearing, and afterwards its size increases with the direction of motion inverted. This phenomenon delimits a boundary between low and high frequency of the external excitation.

Effect of cerium on structure modifications of a hybrid sol-gel coating, its mechanical properties and anti-corrosion behavior

An organic-inorganic hybrid coating was developed to improve the corrosion resistance of the aluminum alloy AA 2024-T3. Organic and inorganic coatings derived from glycidoxypropyltrimethoxysilane (GPTMS) and aluminum tri-sec-butoxide Al((OBu)-Bu-s)(3), with different cerium contents, were deposited onto aluminum by dip-coating process. Corrosion resistance and mechanical properties were investigated by electrochemical impedance measurements and nano-indentation respectively. An optimal cerium concentration of 0.01 M was evidenced. To correlate and explain the hybrid coating performances in relation to the cerium content, NMR experiments were performed. It has been shown that when the cerium concentration in the hybrid is higher than 0.01 M there are important modifications in the hybrid structure that account for the mechanical properties and anti-corrosion behavior of the sol-gel coating. (C) 2012 Elsevier Ltd. All rights reserved.

Chaotic vibrations of a nonideal electro-mechanical system

Nonideal systems are those in which one takes account of the influence of the oscillatory system on the energy supply with a limited power (Kononenko, 1969). In this paper, a particular nonideal system is investigated, consisting of a pendulum whose support point is vibrated along a horizontal guide by a two bar linkage driven by a DC motor, considered to be a limited power supply. Under these conditions, the oscillations of the pendulum are analyzed through the variation of a control parameter. The voltage supply of the motor is considered to be a reliable control parameter. Each simulation starts from zero speed and reaches a steady-state condition when the motor oscillates around a medium speed. Near the fundamental resonance region, the system presents some interesting nonlinear phenomena, including multi-periodic, quasiperiodic, and chaotic motion. The loss of stability of the system occurs through a saddle-node bifurcation, where there is a collision of a stable orbit with an unstable one, which is approximately located close to the value of the pendulum's angular displacement given by alpha (C)= pi /2. The aims of this study are to better understand nonideal systems using numerical simulation, to identify the bifurcations that occur in the system, and to report the existence of a chaotic attractor near the fundamental resonance. (C) 2001 Elsevier B.V. Ltd. All rights reserved.

Mechanical and electrical driving field induced high-frequency dielectric anomalies in ferroelectric systems

Polycrystalline or single-crystal ferroelectric materials present dielectric dispersion in the frequency range 100 MHz-1 GHz that has been attributed to a dispersive ( relaxation-like) mechanism as well as a resonant mechanism. Particularly in 'normal' ferroelectric materials, a dielectric response that is indistinguishable from dispersion or a resonance has been reported. Nevertheless, the reported results are not conclusive enough to distinguish each mechanism clearly. A detailed study of the dielectric dispersion phenomenon has been carried out in PbTiO3-based ferroelectric ceramics, with the composition Pb1-xLaxTiO3 (x = 0.15), over a wide range of temperatures and frequencies, including microwave frequencies. The dielectric response of La-modified lead titanate ferroelectric ceramics, in 'virgin' and poled states, has been investigated in the temperature and frequency ranges 300-450 K and 1 kHz-2 GHz, respectively. The results revealed that the frequency dependence of the dielectric anomalies, depending on the measuring direction with respect to the orientation of the macroscopic polarization, may be described as a general mechanism related to an 'over-damped' resonant process. Applying either a uniaxial stress along the measurement field direction or a poling electric field parallel and/or perpendicular to the measuring direction, a resonant response of the real and imaginary components of the dielectric constant is observed, in contrast to the dispersion behavior obtained in the absence of the stress, for the 'virgin' samples. Both results, resonance and/or dispersion, can be explained by considering a common mechanism involving a resonant response (damped and/or over-damped) which is strongly affected by a ferroelastic-ferroelectric coupling, contributing to the low-field dielectric constant.

Escape in a nonideal electro-mechanical system

In this work a particular system is investigated consisting of a pendalum whose point of support is vibrated along a horizontal guide by a two bar linkage driven from a DC motor, considered as a limited power source. This system is nonideal since the oscillatory motion of the pendulum influences the speed of the motor and vice-versa, reflecting in a more complicated dynamical process. This work comprises the investigation of the phenomena that appear when the frequency of the pendulum draws near a secondary resonance region, due to the existing nonlinear interactions in the system. Also in this domain due to the power limitation of the motor, the frequency of the pendulum can be captured at resonance modifying completely the final response of the system. This behavior is known as Sommerfield effect and it will be studied here for a nonlinear system.

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.

COMPARISON BETWEEN MECHANICAL PROPERTIES AND MICROSTRUCTURE OF ALLOY TI-6AL4V, COLD WORK VERSUS PROTOTIPES BY DIRECT METAL LASER SINTERING

The present work aims to study the microstructure and mechanical properties of titanium alloys, widely used in the manufacture of orthopedic implants in order to compare a new manufacturing technology of implants, rapid prototyping in metals with conventional manufacturing processes. Rapid prototyping is being used in many areas of human knowledge to assist in the study and often in the manufacture of components for their own use. Nowadays with the advancement of software and equipment such as computed tomography and magnetic resonance imaging, we can reproduce any part of the human body in three-dimensional images with great perfection and it is used in the reproduction of implants, scaffolds, material aid and preparation in surgery. This work aims to do: A comparison between the microstructure of the alloy in the two manufacturing processes (prototyping and conventional), showing the grain size, the nature, form, quantity, and distribution of various ingredients or certain inclusions and study of mechanical properties of titanium in both cases.

Clinical study on survival rate of short implants placed in the posterior mandibular region: resonance frequency analysis

Short implants are increasingly used, but there is doubt about their performance being similar to that of regular implants. The aim of this study was to compare the mechanical stability of short implants vs. regular implants placed in the edentulous posterior mandible. Twenty-three patients received a total of 48 short implants (5 × 5.5 mm and 5 × 7 mm) and 42 regular implants (4 × 10 mm and 4 × 11.5 mm) in the posterior mandible. Patients who received short implants had <10 mm of bone height measured from the bone crest to the outer wall of the mandibular canal. Resonance frequency analysis (RFA) was performed at time intervals T0 (immediately after implant placement), T1 (after 15 days), T2 (after 30 days), T3 (after 60 days), and T4 (after 90 days). The survival rate after 90 days was 87.5% for the short implants and 100% for regular implants (P < 0.05). There was no significant difference between the implants in time intervals T1, T2, T3, and T4. In T0, the RFA values of 5 × 5.5 implants were higher than values of 5 × 7 and 4 × 11.5 implants (P < 0.05). A total of six short implants that were placed in four patients were lost (three of 5 × 5.5 mm and three of 5 × 7 mm). Three lost implants started with high ISQ values, which progressively decreased. The other three lost implants started with a slightly lower ISQ value, which rose and then began to fall. Survival rate of short implants after 90 days was lower than that of regular implants. However, short implants may be considered a reasonable alternative for rehabilitation of severely resorbed mandibles with reduced height, to avoid performing bone reconstruction before implant placement. Patients need to be aware of the reduced survival rate compared with regular implants before implant placement to avoid disappointments.