Diffusion systems showing consistent behavior

The behavior of such a large system as a pore formed by a bacterial porine (E. coli OmpF) has been simulated in a lipid bilayer of palmitoyloleoylphosphatidylethanola-mine (POPE) [95]. Despite the use of united atoms, the final system of the trimeric porin embedded into 318 POPE molecules and solvated with water consisted of more than 65 000 atoms in total. During the 1 ns of the MD simulation the trimeric structure remained stable, with almost all flexibility in the loops and turns outside the 3-strands. The movement and orientation of the water molecules was investigated in detail. As found in case of the pore formed by the hexameric LS3 helix bundle [90], the diffusion of the water was decreased to about 10% of that of bulk water. Some ordering of the water molecules was evident from the average water dipole moments, which showed a strong dependence on the vertical position within the porine. 

Regarding the dependence of the reaction efficiency on the dimensionality of the compartmentalized system, the studies reported in Sections III.B.3 and III.B.4 on processes taking place on sets of fractal dimension showed that, consistent with the results found for spaces of integer dimension, the higher the dimensionality of the lattice, the more efficient the trapping process, ceteris paribus. Processes within layered diffusion spaces, which can be characterized using an approach based on the stochastic master equation (4.3), show a gradual transition in reaction efficiency from the behavior expected in c( = 2 to that in = 3 as the number k of layers increases from fe = 1 to k = 11. 

For both 0f and pf, there is one behavior at c < c, a crossover at approximately the same concentration for all parameters, and a distinct behavior at c > c. The phenomenology is entirely consistent with a system that has two fundamentally different dynamical behaviors separated by a dynamic crossover at c. There is no indication in the region c < c that one has a series of different behaviors linked by crossovers. Our experimental results based on optical probe diffusion confirm the interpretation of Phillies and Quinlan that r (c) of HPC solutions shows a sharp dynamic transition at a concentration c" 6 g/L. 

The y precipitates are equiaxed when small, then non-equiaxed as they grow and eventually become plate-like shaped. The y precipitates transform into plates far more readily than y precipitates, which is attributed to the absence of anti-phase boundaries in the Y phase. Despite the non-equiaxed shapes, (r)3 depends approximately linearly on aging time t. The experiments show that the kinetics of coarsening of y precipitates is much slower than that in the reverse system. This is consistent with behavior expected from diffusion in the two phases. 

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