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.

Nonlinear optical absorption of antimony and lead oxyhalide glasses

The optical limiting behavior and nonlinear optical properties of antimony and lead oxyhalide glasses were discussed. The large nonlinear absorption coefficients which range from 11 to 20 cm/GW was determined using standard Z-scan technique. The photodarkening in the samples were observed which suggested that they can also be useful for inscribing Bragg gratings using green lasers of moderate power.

Nonlinear dynamics of short traveling capillary-gravity waves

We establish a Green-Nagdhi model equation for capillary-gravity waves in (2+1) dimensions. Through the derivation of an asymptotic equation governing short-wave dynamics, we show that this system possesses (1 + 1) traveling-wave solutions for almost all the values of the Bond number θ (the special case θ=1/3 is not studied). These waves become singular when their amplitude is larger than a threshold value, related to the velocity of the wave. The limit angle at the crest is then calculated. The stability of a wave train is also studied via a Benjamin-Feir modulational analysis. ©2005 The American Physical Society.

Adsorption of dihydrogen phosphate ion on platinum electrodes in aqueous media monitored by probe-beam deflection

Probe-beam deflection (PBD) was used to monitor concentration gradients of anions adjacent to the surface of a platinum electrode in acidic aqueous media containing H3PO4. PBD can measure the potential-dependent extent of adsorption of H2PO4- on the Pt electrode surface and permits the Langmuir isotherm to be fitted to the experimental data. The value thus obtained for the surface concentration was 1.3 × 10-11 mol mm -2, or 1.7 atoms of Pt per H2PO4-. Also, the electron transfer number obtained was 0.24, signifying an incomplete transfer of charge, and the equilibrium constant is 1.80 suggesting a reversible adsorption process. © 2005 Elsevier B.V. All rights reserved.