Time-scale limitations

We will find it convenient to consider for the moment the special case of perfectly reflecting walls. In the long time-scale limit A a /D, the average propagator for fully restricted diffusion has a simple relationship to the pore geometry. This requirement on A, also known as the pore equilibration condition, implies that the time is sufficiently long that most molecules have collided with the walls. Under this condition the conditional probabilities are independent of starting position so that P(r, t I r, 0) reduces to p(r ), the pore molecular density function. 

Maroudas and co-workers have described a hierarchical scheme for atomistic simulations involving the use of electronic structure calculations to develop and test semiempirical potentials that are in turn used for MD simulations. These results can sometimes be used to develop elementary step transition probabilities for use in dynamic Monte Carlo schemes. With Monte Carlo techniques, the well-known length and time scale limitations of MD can be greatly extended. This hierarchical approach appears to have great promise for the development of simulation strategies that will allow studies of a wide range of practical surface and thin-film chemical and physical processes. 

In the 2D-IR experiments there exists a useful simplification of the description of the spectra when the vibrational dynamics is in the separation of time-scales limit of the so-called Bloch dynamics. Then the correlations of the fluctuations of the various quasi-degenerate amide modes dominate the signals and the interpretations are quite straightforward and analytic. On the basis of experimental determinations of the correlation functions, we explore some of the sensitivities of the 2D-1R signals to the dynamic approximations. In addition, we discuss some of the important possible manipulations of the 2D-IR spectra that permit the display of essentially all possible third-order nonlinear responses from a single data set. 

The present average POl concentration of deep ocean water is 2.2//mol/kg. When a parcel of deep water is transported to the photic zone, this P04 is completely incorporated into plants. Note that this assumes that net primary productivity is not limited by the availability of other micronutrients. In shortterm laboratory studies, this assumption is clearly not true in that it has been demonstrated that the availability of fixed N limits production. Because certain organisms are capable of fixing N from the large N2 gas pool, whereas there is no alternative source or substitute for P04 , it is likely that on longer time-scales, limits productivity. Be-... 

At the mesoscopic scale, interactions between molecular components control the self-organization phenomena between molecular components that lead to random phase-segregation during fabrication of CLs [7]. Mesoscale simulations can describe the morphology of heterogeneous materials and rationalize their effective properties beyond length- and time-scale limitations of atomistic simulations. A recently introduced computational method allows evaluation of the key faetors during fabrication of CLs. These simulations rationalize structural... 

Most of the reaction path approaches make use of a spatial step and accordingly are not affected by the time-scale limitation of other MD methods. For complex systems, however, the ruggedness of the potential energy surface limits the applicability and accuracy of these paths because the number of conformations in the trajectory needs to increase. Another fundamental limitation is that these methods are not applicable for the study of molecular events for which very few details are known about the conformations of products or key intermediates. It is for those processes where theoretical approaches are more helpful. 

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