Inner cutoff length

Here, the actual thickness of adsorbed molecule layers /ad is obtained by multiplying n by adsorbed molecule diameter a0. The actual thickness range in which the fractal geometry is satisfied represents the length-scale cutoff range of fractality.116,118 Here, the value of the lower (inner) cutoff length tadjmfa is equal to... 

The existence of an inner cutoff length has important consequences with respect to the evaluation of the dimensions of natural fractals. All the dimensions described in Section 2.3, except the similarity dimension, require a passage to a limit (e.g. limit... 

Here, F is the gamma function, X is the length corresponding to the inner cutoff for the fractal electrode, A is the macroscopic area, and y is a geometric factor close to l/m. The dimensionless function x(a) can be determined numerically. 

The polyethersulfone capillary ultrafiltration membranes (Daicel Chemical Industries, Ltd., inner diameter 0.8 mm, outer diameter 1.3 mm, length 40 cm, molecular weight cutoff 150 000, water permeability 3 x 10 m m s kPa at 298 K) were used. The length and area of membrane consisting of seven hollow fibers are 40 cm and 70 cm. ... 

Therefore, we can define a length scale range where the rough surface shows the fractal behavior by determining the inner and outer cutoffs using Eq. (28).121 In other words the fractal dimensions determined from the power relation between 7peak and... 

The power-law behavior represented by Eq. (16) is valid between the spatial cutoffs X- and Xa corresponding to the temporal inner (shorter) cutoff ri and the temporal outer (longer) cutoff ro. So far as the diffusion process is concerned, the diffusion layer length acts as a yardstick length.122 Therefore, the relationship between the temporal and spatial cutoffs is given as121... 

In order to test the speed of the D C method relative to conventional MO, single-point PM3 calculations were carried out on a series of a-helix polyalanine structures. Standard bond lengths and bond angles were used for each peptide unit, with a C-C-N-C torsional angle of —57° and an N-C-C-N torsional angle of —47°. In the D C calculations, inner and outer buffer layers of 4.0 A and 2.0 A were used, along with a matrix cutoff of 7.0 A. All computations were performed on a 32-Mbyte IBM RS/6000 Model 370 running AIX version 4.1. 

The hollow-fiber membrane bioreactor took the simple cylindrical geometry housing [dimension 13 mm inner diameter (ID) x 22 mm outer diameter (OD) x 40 mm L see Fig. 14.2]. Cellulose acetate hollow-fiber membranes [200 p,m ID, wall thickness of 14 p,m and molecular weight cutoff (MWCO) of 10 kDa] derived from hemodialysers used to construct the HFMBs. The hollow-fiber membranes were fixed in the bioreactor by using molded silicon rubber. The effective length of the fiber in the reactor was 30 mm with approximately 200 fibers in each bioreactor. The distance between adjacent fibers was approximately 400 p-m, of the order of the distance between natural blood capillaries in human bone. The volume external to the hollow fibers in each HFMB was approximately 3.5 mL, and this volume was available for the collagen gel together with the microcarriers with adherent cells. 

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