Zero crossing period

Tz, zero crossing period = mean period of all the waves in the record. 

The following relationship derived from the sea state statistics in Section 7.1.5 was used to calculate the zero crossing period. 

Significant wave height and zero crossing period... 

Phase-modulation immunoassay measurements are made with sinusoidally modulated light. Since the emission is a forced response to the excitation, the emitted light has the same periodicity as the excitation. Due to the time lag between absorption and emission, the emission is delayed in comparison with the excitation. The time delay between the zero crossing of one period of the excitation and of the emission is measured as the phase angle (Figure 14.11). The emission is also demodulated, due to a decrease in the alternating current (AC) component of the AC to direct current (DC) ratio. 

Figure 21.15 shows the transient response of the measured pressure shortly before and after the onset of the control. In Fig. 21.15, the apparent frequency of the oscillations was deduced as a function of time by measuring the zero crossing. Two sets of data are plotted since every other zero crossing corresponds roughly to one period of oscillation. The curve fit coincides with the average of the two. Figure 21.15c shows the resulting phase shift associated with the frequency change in Fig. 21.15. At about 40 ms after the control was turned...

A parameterization of the JONSWAP spectrum has been worked out by Houmb and Overvik (1976). This work gives recommended values of a, y, and f, when the significant wave height 77 and average zero crossing wave period are given (Table 7.6). 

The problem of deriving the pdf of zero-crossing wave periods is very difficult. Rice derived a pdf for the zero-crossing interval. He treated the interval where I t) [Eq. (7.1)] crosses the 0 line upward at t = 0 and crosses the 0 line downward between r and t - - dr. 

The applications of the periodic wave theory for zero-crossing wave properties raise problems. There have been very few studies about the physical properties of zero-crossing waves, of wave period-wavelength/celerity, of wave height/period — water particle velocities, etc. 

Mean zero up-crossing period at the peak of the storm, Tp. 

The laser can generate a signal to measure an intensity datum every time the amplitude of the cosine wave is zero. The event is known as a zero crossing, and it occurs twice during the period of each cosine wave, or once every 0.3164 urn for the He-Ne laser. A data point collected every 0.3164 urn enables data acquisition up to 15,804 cm-1, so when a routine infrared spectrum is being acquired to about 3800 cm l, data points need be taken only once every four zero crossings. 

This formula, however, tacitly supposes that the instanton period depends monotonically on its amplitude so that the zero-amplitude vibrations in the upside-down barrier possess the smallest possible period 2nla>. This is obvious for sufficiently nonpathological one-dimensional potentials, but in two dimensions this is not necessarily the case. Benderskii et al. [1993] have found that there are certain cases of strongly bent two-dimensional PES when the instanton period has a minimum at a finite amplitude. Therefore, the cross-over temperature, formally defined as the lowest temperature at which the instanton still exists, turns out to be higher than that predicted by (4.7). At 7 > Tc the trivial solution Q= Q Q is the saddle-point coordinate) emerges instead of instanton, the action equals S = pV (where F " is the barrier height at the saddle point) and the Arrhenius dependence k oc exp( — F ") holds. 

---