Fractal interpretations consistent with

Fractal Interpretation Consistent with Known Properties of Globular Proteins... 

We mentioned the possibility of permeability being distributed as a fractal in conjunction with Figure 10. A fractal distribution would show C decreasing moiiotonically at a rate prescribed by its factal dimension. This is not the case with the eolian outcrop which clearly shows two scales of heterogeneity. Given its correspondence with the geologic features, the two-scale interpretation is the only possible consistent interpretation. 

We think that ion channels have the physical properties suggested by the fractal interpretation because the fractal properties are so clearly present in the experimental data, and these properties are consistent with the extensive experimental and theoretical studies of globular proteins. However, this issue can only be resolved by future work that includes X-ray diffraction and NMR, which are needed to determine the three-dimensional structure of the channel protein at high resolution molecular dynamic simulations, which are needed to determine the dynamics of the motions within the channel and molecular biology, which can test our ideas of channel structure and dynamics by purposeful alterations of the channel. 

We view the well established microporous and microfibrillar character of cellulose cotton fibers to support our fractal interpretation. The behavior of the SAXS scattering function is consistent with this fractal interpretation and does not conform to the usual Guinler and Porod methods of analysis. We hope the appoach used in this study is sufficiently provocative to stimulate the thinking of other researchers regarding the growth process of cotton cellulose, whether it be via aggregation of microcrystallites followed by some rearrangement or another process. 

Figure 5 shows the distribution obtained from SAXS measurements of three Los Alamos produced nano-aluminums. The dispersal media for the SAXS measinements is air. Based upon the SEM images, a model of mass fractal aggregates was used to interpret the scattering data (see Fig. 2 for exanqile). This model was found to be consistent with the SAXS data. The volume-weighted size distribution obtained from the analysis is shown. 

The trapping process was simulated using a torus centered around each repeat unit in the cyclic.Any empty torus was considered a pathway for a chain of specified diameter to thread and then incarcerate the cyclic once the end-linking process has been completed. Simulations were consistent with experimental trapping efficiencies. It is possible to interpret these experimental results in terms of a power law for the trapping probabilities and fractal cross sections for the PDMS chains. 

We interpret that the ribbons in the swollen pellicles consist of MFs oriented parallel to the ribbon axis as illustrated in Figure 12 (b-3). The power-law exponent si=2.35 (Figures 11 and 12(a)) reveals that mass centers of the MFs are fluctuating in the lateral direction perpendicular to the ribbon axis with the lateral mass fractal dimension Om l = si - 1 = 135. The mass fractal distribution of the MFs in the lateral direction has the upper cutoff length Ls2=2n/ ( s2 600nm and the low cutoff length Lsi = 2n/[Pg.393]

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