Exponential discharge curve

A problem with Debye theory and the use of ideal components in the equivalent circuits has been that most dielectrics actually do not follow an exponential discharge curve, but a fractional power discharge curve. This law is called the Curie — von Schweidler s law (Schweidler, 1907). We shall revert to this phenomenon later in Section 9.2.12. 

Many dielectrics do not show exponential discharge curves, but fractional power curves. This has led to new models of Universality (see Section 9.2.12). 

Jonscher (1983, 1996) was very well aware of the discrepancy of dielectric discharge curves in the time domain. The Debye model was based upon supposed exponential discharge curves, but most dielectrics actually show fractional power law discharge curves. Because most dielectrics follow fractional power law behavior, such behavior was called the universal behavior. 

Mathematical analyses of EEG SWA have yielded quantitative information about the time course of accumulation and discharge of sleep need. The dynamics of the sleep/wake-dependent changes in delta power have been quantified with the use of computer simulations, and delta power can now be predicted in detail. The increase of sleep need during waking can be described by an exponentially saturating curve with a time constant (Tj) of 18.2 hr in humans (37) and 8.6 hr in... 

The exponential charging and discharging curves of the CR circuit described in Example 1 may also be drawn to scale by following the procedure described below and as shown in Fig. 3.78. 

A discharging exponential curve takes ln(1/x) time constants to reach x times the initial value (or 2.303 time constants for 10%), so... 

Figure IB. Corresponding computed pore population distribution (probability density), n(r, t) (16). Each curve is labeled by the corresponding value of the injected charge Q. For Q = 25 and 20 nC (cases for which REB occurs), N increases to about 108 in less than 0.5 pus and then decays exponentially with a time constant of 4.5 pus. For Q — 15 nC, N increases rapidly to about 105 and remains almost constant for about 4 pus before the exponential decrease. For Q — 10 nC, N increases to about 2 X 103 in about 5 pus and remains almost constant for about 30 pus before the decay phase. The membrane in this case ruptures. For Q = 5 nC, N increases to about 40 in 80 pus. N will return to its initial value as the membrane discharges with a time constant of about 2 s.

In the first extended discussion of H spin-lattice relaxation in a-Si H, Carlos and Taylor (1980) described a characteristic minimun in the temperature dependence of near 40 ° K, which occurs in all glow-discharge deposited samples studied to date. Typical data (Taylor and Carlos 1980 Carlos and Taylor, 1982b) are shown in Fig. 10 for relatively pure samples (top curves) and samples containing 0.5 -2 at. % oxygen (bottom curves). The decays at any given temperature are exponential over one or two orders of magnitude. 

---