Optimization delay time

Casdagli et al. discussed some guides for choosing the optimal delay time x in terms of two concepts, redundancy and irrelevance [81]. Here let us explain their statements by using the Lorenz equation ... 

In general, the energy gap between the electronic states is different in the Franck-Condon (FC) region of the reactants and the products and the wavelengths for pump and dump pulse should be suitably adapted. The optimal delay time At between pump and dump pulse must match the reaction time, in this scenario the time... 

The overall performance is limited by the average 1/NC and 2./NC scalar coupling values that are 10.9 (9.6) Hz and 8.3 (6.4) Hz in the (1-sheet structures (a-helical structures), respectively.37 Consequently the delay 2Ta is routinely set to 25 ms. Assuming that the 15N spin-spin relaxation time for the TROSY component is 50 ms, the transfer efficiency for the intraresidual pathway, for the first t increment (/, =0), is 0.132, when we have optimized delays for the optimal intraresidual transfer in a-helices (Fig. 6). Throughputs for the sequential pathway then become 0.045 (0.058 (5-sheet). 

Re-evaluation of pulse delay times used to record fullerene 13C NMR spectra revealed that a 16 s pulse delay, twice the value for a standard detection, allowed the observation of a weak resonance in the sp3 region at 90.4 ppm in the 13C NMR spectrum of the unlabeled heterofullerene 114. Attempts were made to optimize the NMR experimental parameters for a long 7 i, i.e. the variation of delay times and pulse angles. Various conditions were tried on the labeled material without success. This is probably due to the mixture of the labeled and unlabeled 114 which give too low S/N for signal detection. Table 49 summarizes the NMR results obtained and illustrates a distinct pattern of the azafullerenes. 

Suppose that you have optimized a gradient on a 0.46 X 25 cm column and you want to transfer it to a 0.21 X 10 cm column. The quotient V2/V is ( nr2L)2/( nr1L), where r is column radius and L is column length. For these columns, V2/Vj = 0.083. Equation 25-8 tells us to decrease the volume flow rate, the sample mass, and the delay time to 0.083 times the values used for the large column. The gradient time should not be changed. 

The phase and amplitude spectrum of the laser pulse are tailored to create a wave packet with selected properties. The various eigenstates that comprise the wave packet are populated by different frequency components of the laser pulse, each with its specified amplitude and phase. For example, rovibrational wave packets of Li2 in the El E+ state were created, consisting of vibrational levels v = 12-16 and rotational levels J = 11, 19. The phases and amplitudes of the pump pulse shown in Fig. 20 were generated with a 128-pixel liquid crystal SLM. The pulse was tailored to optimize the ionization signal at a delay time of 7 ps. The phases used to maximize or minimize the ionization signal are shown by solid and dashed lines, respectively, and the intensities at the eigenfrequencies of the wave packet are indicated by circles. 

Fig. 14.2 Comparison traces for the N9 amide resonance of strychnine top) trace extracted from a 3-16 Hz optimized IMPEACH-HMBC experiment bottom) trace extracted from a conventional 8 Hz optimized GHMBC spectrum. Parameters were adjusted to give equivalent data matrices, the only difference being total acquisition time because of the difference between the statically optimized delay in the case of the GHMBC experiment and the accordion-optimized delay in the IMPEACH-MBC experiment [36]. While the...

Figure 7 Davies ENDOR pulse sequence. The upper level indicates the microwave pulses and immediately helow delay times are indicated. The lowest level indicates the rf pulse. Typical times are given based on a 35 GHz spectrometer. The timing of the microwave and rf pulses is less commonly altered, hut the delay time T and the repetition time need significant adjustment to optimize spectral appearance of a given sample. Microwave phase cycling is also employed, hut is not indicated in the figure...

The embedding theorem holds irrespective of the choice of the delay time x, but, in practice, the observed time series are always contaminated by noise, computer round-off errors, or a finite resolution of observations, and they are sampled up to a certain finite time. This requires us to choose an optimal time delay x for an observable s. 

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