Medium fractal geometry

The majority of studies of fractal geometry of bacteria and unicellular fungi (yeasts) have been performed in agar culture, in which the solidity of the medium, nutrient concentration, inhibitory chemicals and incubation conditions (temperature) have been varied. With regard to bacterial pathogens, Escherichia coli, Citrobacter freundii, Klebsiella pneumoniae, Proteus mirabilis. Salmonella anatum. Salmonella typhimurium and Serratia marcescens produced colonies with Dbm values between 1.7 and 1.8 [22, 23], whereas Klebsiella ozaenae had more open colonies, Dbm = 1.6 [24]. Colony morphology is dramatically affected by nutrient supply [19, 20] and nonlethal concentrations of antibiotics [5]. For example, the fractal dimension of... 

The inclusion of 2 extends the previously reported procedure of Relaxation Spectrum Analysis (44). in this form can include contributions from static disorder such as porosity (45), random mixture of conductor and insulator that can be described by the effective medium approximation at percolation (46), or an interface that can be described by a fractal geometry (47). It can also include contributions from dynamic disorder such as diffusion. To provide one specific example if originates from diffusion capacitance in the semiconductor, then r is the minority carriers diffusion time, n = 0.5 and... 

Close to the gel point, the equation m oc shows that the clusters forming the "polymolecular medium" are described in terms of fractal geometry. The fractal domain corresponds to scaling lengths included between the monomer size and the correlation length, which varies as the size of the largest cluster (20). If the fractal dimension describes the way the object occupies the volume, however, it gives no indication on the connectivity. Then, a spectral dimension, ds, was introduced (1,2) which reflects connectivity and takes into account the diffusion as well as the transfer phenomena in the network. This spectral... 

On scales n > 5 (Fig. 43) the Hall properties do not depend on the scale that is, Euclidean geometry prevails. Here the composite can be described as a quasihomogeneous ( gray ) medium, whose properties correspond to effective values of properties. When n 5, a transformation between a fractal and a quasihomogeneous mode of behavior of Hall properties exists. In other words, the scale n = 5 determines the correlation length ,. 

The anomalous diffusivity described by Eq. [13] is due entirely to the fractal nature of the diffusing particle s trajectory in free space. In fractal and multifractal porous media, the diffusing particle s trajectory is further constrained by the geometry of the pore space (Cushman, 1991 Giona et al., 1996 Lovejoy et al., 1998). As a result, when fractional Brownian motion occurs in a two-dimensional fractal porous medium, De becomes scale-dependent, as described by the following equation (Orbach, 1986 Crawford et al., 1993),... 

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