Number of Time Increments

In homonuclear correlation experiments, swi is almost always set equal to sw2- In addition, reduced spectral widths are used in both dimensions to improve digital resolution. The reduced sw s are set equal to the distance between the highest- and lowest-frequency signals. 

Because np2 is so much smaller than the number of points in an ordinary 1D spectrum, whereas SW2 is not commensurately smaller than common ID spectral widths, two-dimensional acquisition times typically are in the 100-300-ms range for H-detected, and less than 100 ms for heteronuclear-detected, 2D experiments. Remember that, as in ID experiments, sw2 (in Hz) depends on the magnetic-field strength and, therefore, affects the value of Similarly, is normally set by the spectrometer after np2 and sw2 have been selected. 

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Figure 3.16 Results of the explicit difference scheme applied to the following diffusion problem (a) initial concentration equal to unity (b) end concentrations at x=0 and x=lcm are zero (c) =0.005cm2 s 1. Length increment is Ax=0.25, i the number of length increments. Time increment is At = 2.5 s, j the number of time increments.

X =6 sqrt(IE-5 T) (The diffusion layer assuming D IE-5 nt =800 A default number of time increments area =0.01 delt =T/nt ... 

The step-function method is based on incrementalization of the total time of the voltammetric experiment t by dividing it into finite equal time increments of width J, and assuming that the unknown functions, (cr)x=o andl(t) can be regarded as constants within each time interval. In (A.27), m is the serial number of time increments, ranging from 1 to M, where M is the total number of time increments, i.e., Md = t. Furthermore, and / are the discrete values of the unknown... 

With 2D experiments the situation is a little more complicated as the size of the overall digitised matrix depends on the number of time increments in tl as well as parameters specific to the 2D acquisition mode. Nevertheless, a digitised matrix of TD(2) X TD(1) complex data points is acquired and stored. Similar to ID the effective number o measured data points used for calculation TD(used) and the total number of data points SI to be transformed in t2 and tl may be defined prior to Fourier transformation. These parameters may be inspected and defined in the General parameter setup dialog box accessible via the Process pull-down menu. With 2D WIN-NMR the definitions for TD(2) and TD(1) are the same as for TD with ID WIN-NMR. However, unlike ID WIN-NMR, with 2D WIN-NMR SI(2) and SI(1) define the number of pairs of complex data points, instead of the sum of the number of real and imaginary data points. Therefore the 2D FT command (see below) transforms the acquired data of the current data set into a spectrum consisting of SI data points in both the real and the imaginary part. 

Thus, if the temperatures of the various nodes are known at any particular time, the temperatures after a time increment At may be calculated by writing an equation like Eq. (4-28) for each node and obtaining the values of 7V1- The procedure may be repeated to obtain the distribution after any desired number of time increments. If the increments of space coordinates are chosen such that... 

We find this calculation in substantial disagreement with the results of Example 4-10. With a larger number of time increments better agreement would be achieved. In a problem involving a large number of nodes, the implicit formulation might involve less computer time than the explicit method, and the purpose of this example has been to show how the calculation is performed. 

To determine the steady-state distribution we could carry the unsteady method forward a large number of time increments or use the steady-state method and an iterative approach. The iterative approach is required because the equations are nonlinear as a result of the variations in the convection coefficient,... 

Refinements in the Schmidt graphical method are discussed by Jakob [5], particularly the techniques for improving accuracy at the boundary for either convection or other boundary conditions. The accuracy of the method is improved when smaller Ax increments are taken, but this requires a larger number of time increments to obtain a temperature distribution after a given time. 

The N matrix provides the expected number of time increments that the system dwells in each system success state (a transient state) as a function of starting state. In our example, the top row states the number of time... 

Szabo [40-42], An implicit and explicit scheme is employed at alternating points within the two-dimensional mesh (Fig. 5), which allows the new concentrations to be calculated explicitly, but with the advantage of an implicit stability criteria [22], A counter (a sum of the number of time increments plus the i and j pointers) is used to determine whether the calculation is performed explicitly (if the counter is odd)... 

The M Code has numbered each of the peaks that are a certain percentage above the baseline. This percentage is an adjustable parameter. The TIC is divided into a number of time increments. The increment chosen for this discussion is 5 minutes. The code compares the mass qtectrum of each of the numbered peaks within the time increment with the reference library and displays a shaded area for the increment if there is a fit between the sample and reference q)ectra to the degree that is prespecified. The... 

The experiment takes place over a total time t p, so that the value of St will depend on the number of time increments nt ... 

EXPERIMENTAL PARAMETERS THE NUMBER OF TIME INCREMENTS NT AND NUMBER OF SPACE INCREMENTS NS ... 

Feldberg has suggested that fi = 55x that is, the reaction layer should be at least 5 times the grid space size. In terms of the number of time increments, we... 

The number of time increments needed for a simulation then becomes nt = time of experiment x 50 x kchem-... 

Figure 5-1 Simulation of an EC mechanism (Aci,j , = 1000 s" ) with the number of time increments (NT) set to NT = 4 x time x kchem (circles), and NT = 50 x time x (line).

Figure 5-2 Simulation of an ECE mechanism, with the number of time increments set as in Figure 5-1.

Generally, highly accurate results for all mechanisms have been obtained (<0.5 /o error). In any case, it is important to remember that the number of time increments, which determines the accuracy, can be set by the user. For any new mechanism, a test simulation can be done using a more rigorous constraint (use 10 times more time increments than the default) to check for accuracy. 

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