Second-order point process time scale

If the time scale of neutron capture reactions is very much less than 3 -decay lifetimes, then rapid neutron capture or the r process occurs. For r-process nucleosynthesis, one needs large neutron densities, 1028/m3, which lead to capture times of the order of fractions of a second. The astrophysical environment where such processes can occur is now thought to be in supernovas. In the r process, a large number of sequential captures will occur until the process is terminated by neutron emission or, in the case of the heavy elements, fission or (3-delayed fission. The lighter seed nuclei capture neutrons until they reach the point where (3 -decay lifetimes have... 

The essential feature of PC materials is the ultrafast phase transition between amorphous and crystalline structures that occurs on a nanosecond time scale. In the previous sections, we have discussed extensively the amorphous and crystalline structures of GST and their properties. These correspond to the starting and end points for the actual phase transition, which are crucial to understand the function of PC materials. We now present results for the nucleation-driven crystallization process of GST using DF calculations combined with MD [31], A sample of fl-GST with 460 atoms was studied at 500, 600, and 700 K, and a second sample of 648 atoms was simulated at 600 K. In all cases we used a fixed crystalline seed (58 atoms, 6 vacancies) in order to speed up the crystallization process. More recent experience has shown that the time scale for the crystallization is of the order of several nanoseconds for these system sizes in the absence of a fixed seed, while those here are of the order of 0.3-0.6ns. This means that we cannot discuss the onset of nucleation, but this is also true in the case of smaller systems (<200 atoms) discussed by other groups. In very small systems, periodic boundary conditions bias the process severely. Our larger samples reduce finite-size effects, and we show the effect of choosing different annealing temperatures. Simulations of this scale (up to 648 atoms over 1 ns) are near the limit of present day DF/MD calculations. 

The second difference relates to the definition of a cutoff time point for the evaluation of the difference factor and the Rescigno index. When cumulative data are available, evaluation of the difference factor or the Rescigno index usually requires a reference data set in order to define the cutoff time point for index evaluation (30). For the evaluation of fl and the , i.e., when the difference factor and the Rescigno index are evaluated from non-cumulative data, this difficulty does not exist, provided that the release process has been monitored up to the end (i.e., until dissolution of the drug is complete). At this point, it is worth mentioning that a similar conclusion cannot be drawn for the similarity factor (31) because application of this index to non-cumulative data is set apart by the careful scaling procedure required, in addition to the existence of a reference data set. The reason is that this index can continue to change even after dissolution of both products is complete. 

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