Onset Of Relaxation Oscillations Research Articles

The influence of the integral manifold shape on the onset of relaxation oscillations

The relaxation oscillations are studied of a singularly perturbed system of ordinary differential equations with m slow and n fast variables (m × n) in the two cases: (1) m = n = 1 (1 × 1) and (2) m = 2, n = 1 (2 × 1). As sufficient conditions for the existence of relaxation oscillations there some general class is described of the functions determining the slow manifold for this system.

Analysis of the effect of temperature on complex self-oscillation regimes in the belousov-zhabotinskii reaction in a constant-agitation flow-through reactor

Modeling of the influence of temperature on complex self-oscillation regimes in the BZ reaction in a CAFT has been carried out. It is shown that the onset of relaxation oscillations as the temperature is raised results from bifurcation of the onset of an infinite period. The disappearance of the oscillations as the temperature is raised further is due to a Hopf bifurcation. The results of the modeling are in qualitative agreement with the experimental data.

Thermal instabilities and poloidal asymmetries in the tokamak edge plasma

The thermal stability of a collisional, radiating edge plasma in magnetic confinement experiments with respect to marfe-type perturbations is investigated analytically and numerically. The fluid description used includes a non-local electron heat flux model and non-equilibrium impurity radiation cooling. The dispersion relation of a homogeneous plasma is derived analytically, and stability criteria are given. Various experimental scenarios are simulated with a sophisticated numerical model including all the relevant dynamics along field lines and a rough approximation of cross-field transport. The formation and history of global ‘marfes’ and the onset of relaxation oscillations under appropriate conditions are demonstrated. The possible occurrence of more localized perturbations is discussed. The results compare well with those of experiments.

Analysis of the response of lasers to external signal injection

The rate equation including the injection term was extended and solved numerically. The relation between the peak photon number in the onset of relaxation oscillations of lasers and the injected photon number is shown. The step response of the CW laser to the external signal injection and the reshaping property of the laser for the distorted optical pulse are reported.

A New Instrument for the Measurement of Ionising Radiations

A moving coil microammeter of relatively long period is used to integrate the current obtained in an intermittent glow discharge in a rare gas. This gives an indication of the intensity of any ionising radiation which produces an increase in the frequency of the discharges, in the “counting region” between the breakdown potential of the gas and the onset of relaxation oscillations. The method is sufficiently sensitive for the direct detection of cosmic radiation. A description is given of a portable instrument embodying this principle, using headphones to make audible the discharges, which may be employed for the location of lost radium. The application of the method to the measurement of gamma ray activity of radioactive substances, and of the tolerance dose of scattered X rays, is discussed.