Switching-off in a minimal time a fitzhugh-nagumo system

This paper deals with a system that describes an electrical circuitcomposed by a linear system coupled to a nonlinear one involving a tunneldiode in a flush-and-fill circuit. One of the most comprehensive models for thiskind of circuits was introduced by R. Fitzhugh in 1961, when taking on carebiological tasks. The equation has in its phase plane only two periodic solutions,namely, the unstable singular point S0 and the stable cycle Γ. If the system isat rest on S0, the natural flow of orbits seeks to switch-on the process by going- as time goes by - toward its steady-state, Γ. By using suitable controls it ispossible to reverse such natural tendency going in a minimal time from Γ toS0, switching-off in this way the system. To achieve this goal it is mandatorya minimal enough strength on controls. These facts will be shown by means ofconsiderations on the null control sets in the process.

Nitrogen diffusion in niobium under low pressure

The interaction among heavy interstitial atoms present in metals with bcc structure is studied using anelastic spectroscopy. This technique makes it possible to obtain information on interstitial concentration, precipitation, solubility limit, and diffusion. The diffusion coefficients of nitrogen in niobium were obtained using the relaxation parameters obtained from anelastic spectroscopy measurements for different oscillation frequencies of the system. The results showed the interstitial diffusion of nitrogen present in solid solution in niobium when submitted to different charges of nitrogen at a temperature of 1373 K and a partial pressure in the order of 10-4 Torr. The exponential variation of the pressure experimentally in function of the time was thus obtained.