Real-time averaging

To obtain the real time-averaged DEP force for equation (6.223), we use... 

Simulation runs are typically short (t 10 - 10 MD or MC steps, correspondmg to perhaps a few nanoseconds of real time) compared with the time allowed in laboratory experiments. This means that we need to test whether or not a simulation has reached equilibrium before we can trust the averages calculated in it. Moreover, there is a clear need to subject the simulation averages to a statistical analysis, to make a realistic estimate of the errors. 

The molecular dynamics analyzes times steps, also called snapshots (coordinates and velocities), for display, averaging, and plotting (possibly from other applications). In the present release of HyperChem, two particular sources are relevant (the DDE interface allows the possibility of other generators of snapshots as well). The first source are time steps that are computed, displayed, and averaged. This is the normal real-time use of HyperChem molecular dyn amics. 

Besides the deviation mentioned above, the main problem with the dynamical information from the MF approximation is that it contains only one positive frequency and so the resulting real-time correlations cannot be damped or describe localizations on one side of the double well due to interference effects, as one expects for real materials. Thus we expect that the frequency distribution is not singly peaked but has a broad distribution, perhaps with several maxima instead of a single peak at an average mean field frequency. In order to study the shape of the frequency distribution we analyze the imaginary-time correlations in more detail. 

The response functions are obtained as derivatives of the real part of the time-averaged quasienergy Lagrangian ... 

Meteorology Real-time, with hourly averaging... 

In a real-time spectroellipsometric measurement in which the kinetics of a-Si H deposition is studied, trajectories are recorded in the A-4 plane at various photon energies between 2 and 4 eV. These trajectories can be simulated and fitted to models that represent the growing a-Si H layer. Canillas et al. [347] have made a detailed study of the deposition of the first few layers of a-Si H on a NiCr/glass substrate. Similar results are obtained for a c-Si substrate. They have proposed several models to explain the data. One possible model is the hemispherical nu-cleation model, which describes a hexagonal network of spherical a-Si H nuclei located at an average distance d between them. The growth is represented by an... 

The forward prediction x,(m + 1) is computed by averaging the n sample values in the future of the (m + l)st one. Since future data are required, this computation is not possible in real time and hence is noncausal. 

The simulation shown in Fig. 10 is an impact of a saturated water droplet of 2.3 mm in diameter onto a surface of 400°C with an impact velocity of 65 cm/s, corresponding to a Weber number of 15. This simulation and all others presented in this study are conducted on uniform meshes (Ax — Ay — Az = A). The mesh resolution of the simulation shown in Fig. 10 was 0.08 mm in grid size, although different resolutions are also tested and the results are compared in Figs. 11 and 12. The average time-step in this case is around 5 ps. It takes 4000 iterations to simulate a real time of 20 ms of the impact process. The simulation... 

The research on the flow regimes in packed tubes suggests that laminar flow CFD simulations should be reasonable for Re <100 approximately, and turbulent simulations for Re >600, also approximately. Just as RANS models provide steady solutions that are regarded as time averages of the real time-dependent turbulent flow, it may be suggested that CFD simulations in the unsteady laminar inertial range 100 time-averaged picture of the flow field. As with wall functions, comparisons with experimental data and an improved assessment of what information is really needed from the simulations will inform us as to how to proceed in these areas. 

Electroencephalography allows real-time measurement of neural activity with millisecond temporal resolution. When coupled with the repeated presentation of a stimulus, the electroencephalograms can be averaged to produce an event-related potential (ERP), whose components develop and resolve within tens or hundreds of milliseconds. These potentials are designated by the millisecond lag between presentation of the stimulus and the appearance of the ERP, with the P50 (i.e. potential at 50 ms after... 

An uncertainty conscious scheduling approach for real-time scheduling was presented in this chapter. The approach is based on a moving horizon scheme where in each time period a two-stage stochastic program is solved. For the investigated example it was found that the stochastic scheduler improved the objective on average by 10% compared to a deterministic scheduler. 

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