Fractal dimensions and

For a fractal surface D > 2, and usually D < 3. In simple terms the larger D, the rougher the surface. The intuitive concept of surface area has no meaning when applied to a fractal surface. An area can be computed, but its value depends on both the fractal dimension and the size of the probe used to measure it. The area of such a surface tends to infinity, as the probe size tends to zero. 

Physically, the wetting abdity increases (the contact angle decreases) as the values of the fractal dimension of the electrode increases if the electrode material is same. However, in this study, we could not obtain a good correlation between the fractal dimensions and the wetting abilities as shown in Table 1. It means that not only the physical properties such as the surface irregularity and roughness but also the chemical interaction between electrolyte and electrode were important in wetting ability. 

Su-Il Pyun provide a comprehensive review of the physical and electrochemical methods used for the determination of surface fractal dimensions and of the implications of fractal geometry in the description of several important electrochemical systems, including corroding surfaces as well as porous and composite electrodes. 

Here, D< )s is the fractional diffusivity defined as (4-2d,) (2d,-4) )(3-dP) j js a constant related to the fractal dimension and R0 is the side length of a square electrode), and dv dtv means the Riemann-Liouville mathematical operator of fractional derivative ... 

The present article summarized the fractal characterization of the rough surfaces and interfaces by using the physical and the electrochemical methods in electrochemistry. In much research, both the physical and the electrochemical methods were used to evaluate the fractal dimension and they are complementary to each other. It should be stressed that the surface fractal dimension must be determined by using the adequate method, according to the inherent scaling properties of the rough surfaces and interfaces. 

SO that the escape rate can be directly related to the fractal dimension and the Lyapunov exponent ... 

Figure 34. The temperature dependence of the static Ds (A) fractal dimensions and the product 3v ( ). At the percolation threshold temperature (Tp = 26.5°C) Ds = 3v. (Reproduced with permission from Ref. 2. Copyright 2002, Elsevier Science B.V.)...

Diffusion-limited aggregation of particles results in a fractal object. Growth processes that are apparendy disordered also form fractal objects (30). Sol—gel particle growth has also been modeled using fractal concepts (3,20). The nature of fractals requires that they be invariant with scale, ie, the fractal must look similar regardless of the level of detail chosen. The second requirement for mass fractals is that their density decreases with size. Thus, the fractal model overcomes the problem of increasing density of the classical models of gelation, yet retains many of its desirable features. The mass of a fractal, Af, is related to the fractal dimension and its size or radius, R, by equationS ... 

Size and shape factors in combination with fractal dimension and rheological tests provide, prior to preformulation assays, a reliable technique for the appropriate selection of materials and detection of undesirable properties related to shape-surface characteristics. 

Curl, R.L., 1986, Fractal dimensions and geometries of caves. Mathematical Geology, 18 pp. 765-783. 

There are a number of different fractal dimensions commonly used to describe a specific property of a system. These fractal dimensions and methods to obtain them are explained in detail in Boundary and Surface Fractal Dimensions and Mass Fractal Dimension. Fractal dimensions used in specific applications will be shown also in the related section. 

Laser diffraction technique is able to generate the envelope diameter distribution of the aggregates in the aerosol cloud, as well as the surface and mass fractal dimensions as explained in Light Scattering under both Boundary and Surface Fractal Dimensions and Mass Fractal Dimension. However, validation of Eq. (25) by comparison studies between the impaction and laser diffraction techniques is required. 

Three percent of o-limonene was found to cause skin damage. However, instead of roughening, the damage caused smoothing as shown by a decrease of fractal dimension and was suggested to be a result of hydration and/or edema formation in the shallow part of the skin.f Hence fractal analysis can be used to elucidate the damage mechanism and provides quantitative measurement of skin damage. ... 

Magill, J. Fractal dimension and aerosol particle dynamics. J. Aerosol Sci. 1991, 22 (Suppl. 1), 165-168. 

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