Mean arrival time

This reduction in information is achieved by a preprocessor, which uses the digital voltages corresponding to an ion peak to estimate the peak area (ion abundance) and centroid (mean arrival time of peak, equivalent to m/z value) these two pieces of information — plus a flag to identify the peak — are stored. 

Figure 16 Reciprocal mean arrival times versus (cfkT)2, parametric in the number of lattice planes nz.

Figure 18 Mean arrival times versus thickness for different values of olkT.

Figure 5 illustrates different paths that are taken by different parts of the original stream emanating from one point in a fracture network. All the paths will have a different RTD. Each path will have its own mean travel time. When matrix diffusion is active there will also be a spread in residence times along each trajectory such as seen in Figure 5. The mean arrival times for the different trajectories will be different giving rise to velocity dispersion which then is superimposed on the spreading along each trajectory caused by the matrix diffusion effects.

Fig. 6.16. Localization errors resulting from an erroneous arrival time (same arrangement as Fig. 6.15, arrival time at sensor 1 altered by 5 rs) calculated and depicted for an array of 40 by 40 points. Top left actual localization errors as vector Top right, actual localization errors as density function (equidistance 0.01 m) Bottom left mean arrival time residuals as density function (equidistance 0.25 ps) Bottom right major axis of the error ellipsoid.

Figure 2 illustrates two simulated signals A and B with an AR, calculated as in equation 5, of 1.25 and 2.52 corresponding to i/a values of 1 and 4 respectively. These two signals would result from different polymers, in this example corresponding to PEG 1470 and PEG 71(X), under the experimental conditions to be described later. The progress of elution of the overall concentration profile may be characterized by the center of gravity of the profile or mean arrival time defined as... 

Though the mean arrival time is the same for diffi nt polymers, an effective resolution based on the shape of the leading peaks can be calcula using equation 10. Under the experimental conditions reported, a time-based resolution of 0.27 was calculated between PEG 1470 and 7100 (Figure 5). Though a resolution of 0.27 seems small from conventional HPLC separation stands (1), various chemometric techniques can be used to analyze poorly resolved peaks to about 0.10 resolution (12-15). 

The arrival time according to the template is the Initial Berth Time Requested (IBTR) by the vessels. The actual arrival time is stochastically distributed with the IBTR as the mean arrival time. 

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