Time slices

Here, the sums are over different time slices / at which coordinates r and corresponding work values have been saved. 

This sequence of states is a discrete representation of the continuous dynamical trajectory starting from zo at time t = 0 and ending at z at time t = . Such a discrete trajectory may, for instance, result from a molecular dynamics simulation, in which the equations of motion of the system are integrated in small time steps. A trajectory can also be viewed as a high-dimensional object whose description includes time as an additional variable. Accordingly, the discrete states on a trajectory are also called time slices. 

Expected changes are less dramatic in the HIRHAM H model, which projects a reduction of 3.8% for the mean annual precipitation and an increase of 4.2°C for the mean annual temperature. While the two RCMs predict quite different reductions of the mean annual precipitation, with HIRAM H showing only a slight reduction, both models agree in a dramatic increment of the annual temperature for the time-slice 2071-2100, with RCAO E projecting the largest increase with respect to the control period. 

The hydrological simulations for the future time-slice 2071-2100 were performed using the bias-corrected daily time series derived from the two different climate scenarios described in Table 4 as external forcing, and the hydrological parameters obtained during the calibration and verification period described in Sect. 6.1. One operational modification was made to the simulation of subcatchment 057, where a withdrawal corresponding to the Ebro-Besaya water transfer, described in Sect. 6.1, was allowed to remove water outside the catchment. This water transfer was introduced only for the simulations of the future scenarios, while the... 

LC-NMR can also be run in an on-flow mode, where NMR acquisition is started at the chromatography injection and randomly divided into a series of time slices. However on-flow NMR measurement not only suffers from low sensitivity, but LC gradient elution also causes problems on account of the drift of signals relative to the signal lock, where the presaturation frequency of each time slice needs to be defined in a separate run. 

Dextran polymers were used to evaluate the utility of the linear, polydisperse calibration method for water-soluble polymer characterization. A blend of T-40 and T-70 dextran standards was used as a polydisperse calibration standard. Table VIII displays the report from the linear calibration method using this standard. Nine Iterations of the search algorithm were required for convergence to the true and Mn values of the standard. As can be seen in the report, the elution volume profile of the standard contained 72 area/time slices upon which calibration calculations were based. The slice width was set at 10 seconds/siIce. Figure 5 shows a plot of the calibration curve generated from the linear calibration method utilizing the dextran standard,... 

There are four general modes of operation for LC-NMR on-flow, direct stop-flow, time-sliced and loop collection/transfer. The mode selected will depend on the level and complexity of the analyte and also on the NMR information required. All modes of LC-NMR can be run under full automation for LC peak-picking, LC peak transfer to storage loops or NMR flow cell, and NMR detection [46],... 

Time-shcing is a variation of the stop-flow mode where the flow is stopped in a time-dependent manner (e.g. every 15 s) for the whole chromatographic run, in a sense the ultimate approach in slow-flow. When the flow is stopped, sufficient scans can be made to give the desired level of detection before moving on to the next time-slice. The whole process can be automated through software control. There is no requirement for an UV detector, and the approach has been used to identify non-UV-active components in drug substances [48]. The peak purity of... 

First of all, take 1 min time slices. The given data are then... 

Applications of LC-NMR are still scarce but the technique will become more widely used. The main effort for efficient exploitation of LC-NMR needs to be made on the chromatographic side, where strategies involving efficient preconcentration, high loading, stop-flow, time slicing, or low flow procedures have to be developed. Microbore columns or capillary separation methods, such as capillary LC-NMR, CE-NMR, and CEC-NMR, will find increased application, one reason being that the low solvent consumption will allow the use of fully deuterated solvents. 

Fig. 6. The q-integrated photosignal of iodine in methanol from a time-slicing experiment. The red curve is the temporal profile of the x-ray pulse.

The estimates focus on three time slices The current atmosphere (selected as 1992), and two future atmospheric situations 2015 and 2050. Estimates for the 1992 emissions have been given, as well as projections for 2015 (IPCC, 1999). For 2050 very estimates have been made, based on extrapolations of the 2015 estimates. In addition options exists for high or low growth in energy demand, and possibilities for technology improvements. The table below gives the adopted NOx emissions for current conditions (1992,2015), a medium and a high case for 2050 (IPCC, 1999). 

For the time slices 1992 and 2015, two model runs were made A basic scenario with no aircraft emissions, and a scenario with aircraft NOx emissions added (Table 1). For 2050 a model run with a basic scenario and two aircraft runs with the medium and high scenarios were run (Table 1). The model runs are summarised in Table 3. 

The strategies to measure isotope ratios include peak area and peak height ratioing and on a time slice method with calculation of an isotope ratio for each data point separately as shown in Fig. 4. Peak height is not so suitable because of the high shortterm noise of ICP-MS. Best results are obtained for peak area and time slice ratio measurements. 

Fig. 5. Strategies for isotope dilution analysis utilizing on-line coupling IC-ICP-MS. Shown is the separation of bromate and bromide by anion IC.The sample was 585 )Lll of a bottled water, spiked with bromate and a bromate isotope standard. The column, eluent and detection device are as described in Fig. 4. Shown are the mass traces form/z79 and 81 (dotted line) and the total time slice isotope ratio for m/z 79/81.

The analytical NMR flow-cell (see Figure 1.8) was originally developed for continuous-flow NMR acquisition, but the need for full structural assignment of unknown compounds led to major applications in the stopped-flow mode. Here, the benefits of the closed-loop separation-identification circuit, together with the possibilities to use all types of present available 2D and 3D NMR techniques in a fully automated way, has convinced a lot of application chemists [17-70], A detailed description of the different modes for stopped-flow acquisition (e.g. time-slice mode) is found in Chapters 2 und 3. 

It is also worth briefly reiterating here the main operational modes for HPLC-NMR and HPLC-NMR-MS. There are currently five main options which can be employed for HPLC-NMR using either isocratic or gradient elution. These are continuous-flow, stop-flow, time-sliced stop-flow, peak collection into capillary loops for post-chromatographic analysis, and automatic peak detection with UV-detected triggered NMR acquisition. 

Figure 4.5 Typical H LC-NMR data obtained from a time-slice experiment. These data were obtained by stopping flow at 30 s intervals through a chromatographic run from 5.0min into the run through 14.0 min. Each spectrum was acquired for 128 transients...

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