Characteristics fractal

The Pore Structures and Surface Fractal Characteristics of Meso/Macroporous Carbon Specimens I, n, and III Calculated from the Analyses of the N2 Gas Adsorption Isotherms. Reprinted with permission from G. -J. Lee and S. -I. Pyun, Carbon, 43 (2005) 1804. Copyright 2005, with permission from Elsevier. 

On the other hand, it is impossible to apply the SP method to the correct description of gas adsorption in the micropores, since the adsorption in the micropores does not occur by multilayer adsorption but by micropore volume filling process. In this case, the pore fractal dimension gives a physical importance for the description of structural heterogeneity of the microporous solids. Terzyk et al.143"149 have intensively investigated the pore fractal characteristics of the microporous materials using gas adsorption isotherms theoretically simulated. 

In this context, Berry [277] studied the enzyme reaction using Monte Carlo simulations in 2-dimensional lattices with varying obstacle densities as models of biological membranes. That author found that the fractal characteristics of the kinetics are increasingly pronounced as obstacle density and initial concentration increase. In addition, the rate constant controlling the rate of the complex formation was found to be, in essence, a time-dependent coefficient since segregation effects arise due to the fractal structure of the reaction medium. In a similar vein, Fuite et al. [278] proposed that the fractal structure of the liver with attendant kinetic properties of drug elimination can explain the unusual... 

The plot illustrates the increasing population with a similar slope (or power-law, fractal relationship) for the central part of the measured populations. The identification of fractal characteristics is not a simple process and a recent work suggests that using a straight line fit to the log cumulative population data can be misleading. 

Knipe, R.J. and McAllister, E. 1996. Fault population analysis identification of fractal characteristics for scaling. J. Struct. Geol., submitted. 

Altemeier et al. [30] measured the fractal characteristics of ventilation and determined that not only are local ventilation and perfusion highly correlated, but they scale as well. Finally, Peng et al. [31] analyzed the BRV time series for 40 healthy adults and found that under supine, resting, and spontaneous breathing conditions, the time series scale. This result implies that human BRV time series have long-range (fractal) correlations across multiple time scales. ... 

Huang, Z.H., Kang, F.Y., Huang, W.L., et al. (2002). Pore structure and fractal characteristics of activated carbon fiben characterized by using HRTEM. J. Colloid Interface Sd., 249, 453—7. 

Pyun, S.I. and Rhee, C.K. (2004) An investigation of fractal characteristics of mesoporous carbon electrodes with various pore structures. Electrochim. Acta, 49, 4171-80. 

Guerrini, I.A., and D. Swartzendruber. 1994. Fractal characteristics of the horizontal movement of water in soils. Fractals 2 465-468. 

Fracture surface are rough, with certain fractal characteristics. A fracture itself can be seen as congruence of the upper and lower fracture surfaces. 

It is known from fractals theory that, if dimensions of a fracture surface are D, a random Brown function with the exponent of H can produce a fracture surface with fractal characteristics by using the following formula. 

According to a certain D, the curved surface height z of an arbitary point can be obtained if A is given (commonly 1.0 fracture surface with fractal characteristics can be obtained by overall distribution (x,y). Fig. 1 shows a fracture surface generated by simulation using random Brown function method, the fractal dimensions is 2.3 and the parameter A = 1.25. 

From the viscosity versus time data collected for each system, the molecular weight and cluster size can be calculated as a function of time to the gel point using the equations derived in the first few sections of this chapter. From these calculations, it is possible to model the evolution of the gel structure dynamically. In Fig. 11, the evolution of an HF-catalyzed gel as a function of time is presented, starting with the unhydrolyzed monomer molecule tetra-ethoxysilane at time zero and proceeding, in stages, to the final gel structure at 16 minutes. Also presented is the effect of normal drying, in which the fractal characteristics of the individual clusters are all but eliminated. 

Description of Molecular Mobility Using Fractal Characteristics... 

The authors [46] performed the hydro dynamical and molecular characteristics of aromatic copolyethersulfoneformals (PESF) [47] in diluted solutions (the solvents—tetrachloroethane and 1,4-dioxane) determination and their intercommunication with fractal characteristics. Kuhn segment size A for PESF can be determined with the aid of Flory-Fox equation [48] ... 

Research on the fractal characteristics of pore structure of coal particles based on low temperature nitrogen adsorption method... 

THE FRACTAL CHARACTERISTICS OF PORE STRUCTURE OF COAL PARTICLES... 

Jiang Xiumin, et al. 2003. Fractal Characteristic of Surface Structtire of Micro-Pulverized Coal. Proceedings of the Csee, 23(12) 165 169 (in Chinese). 

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