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A fractal is a geometric object with internal homothetic, which it repeats his shape in its same form on different scales.
Despite the simplicity of the definition, the function has a complex shape whose contour is a fractal. It possible to view and draw it only by using a computer.
The fractal dimension [D.sub.f] was calculated by plotting [dS.sub.Hg]/[dp.sub.c] verse [p.sub.c] in a log-log plot.
Based on the thermodynamic analysis of mercury intrusion process and fractal characteristics of pore surface, Zhang and Li [30] proposed a thermodynamic model, and the simplified equation for calculating fractal dimension can be expressed as [31]
The above-modified expressions ((10) and (12)) demonstrate that the damage can be defined by the number of loading cycles and the fractal dimension and also can be defined by acoustic emission parameters in AE caused by fatigue fracture.
Figure 4 demonstrates the voltage standing wave ratio versus frequency plot in GHz of proposed fractal tree-shaped MSA.
Equation (9) represents the fundamental properties of the fractal structure under scale transformation.
This paper considering system of contact model of two rough surface fractal characteristics is in order to make contact more general.
Fractal objects develop via the repetition of the same principles from small scales to large scales.
3 are angularly directed mostly towards the specular direction for low fractal dimensions, while they are more angularly diffused for high fractal dimensions (this was a clear observation of ours for a very large number of computer simulations).
where [L.sub.t](d) is the total length of the tortuous capillary tube and [D.sub.t] is the tortuosity fractal dimension of the capillary path, which lies in the range 1 < [D.sub.t] < 2.