Bistability and Fluctuations for an Incandescent Light Bulb

Abstract

We develop a simple kinetic model to explain the hysteresis that occurs when an incandescent light bulb is controlled by a rheostat in the external circuit. The model is based on changes in the temperature of the filament that are associated with internal energy changes due to radiation and Joule heating. The radiative processes are idealized as occurring via photons lost and gained by a blackbody, while the dynamics of the electric current are treated via the Langevin equation. Quantum corrections to the elementary process description of blackbody radiation are derived. Like the ballast resistor, the model exhibits hysteresis due to a region of bistability of the temperature as a function of the resistance in the rheostat, the criterion for stability being that the temperature of the filament decreases with increasing resistance in the rheostat. Explicitly including variations in the current, we show that temperature and current fluctuations are correlated and that they diverge as the thresholds for stability are approached. It may be possible to study these divergences experimentally.

Simulation of the Fertilization Ca2+ Wave in Xenopus laevis Eggs

“…According to this idea the Ca 2ϩ handling mechanisms in the mature egg can support two alternative physiological Ca 2ϩ concentrations, a low basal concentration typical of the prefertilization state and an elevated concentration typical of Ca 2ϩ behind the wave. Bistability is a well known phenomenon in both reactive chemical solutions and electrical circuits and is associated with hysteresis (Goldbeter, 1996;Keizer et al, 1995a). Bistability has recently been used to describe maturation of the immature X. laevis oocyte (Ferrell and Machleder, 1998) Here we pursue the notion that the bistability of [Ca 2ϩ ] i in the mature Xenopus egg is caused by the same underlying mechanisms responsible for spiral waves in immature Xenopus eggs.…”