Fragmentation fractals

Equation (2.30) amounts to a power-law relationship between N r ) and r , so, as n oo, it defines aprobabilistic fractal. Following Kaye [43], it is occasionally called a fragmentation fractal, and Dftagm is termed the fragmentation fractal dimension. 

Kozak, E., Pachepsky, Y.A., Sokolowski, S., Sokolowska,Z. andSt pniewski,W. (1996). A modified number-based method for estimating fragmentation fractal dimensions of soils. Soil Sci. Soc. Am. J., 60, 1291-1297. 

In order to be normalizable, this distribution can be only valid over the size range / min < R < / max, which is limited by the cut-off values / niin and / max- Such distributions are very important in various applications, and their properties depend strongly on the value of the exponent v. In many situations, the exponent falls into the range of 2 < u < 3, and in such cases it was referred to as fragmentation fractal dimension. Such... 

G. J. Brown, N. J. Miles, The Fragmentation Fractal - A Useful Descriptor of Broken Rock , Part. Part. Syst. Charact., 12(3) (1995) 166-169. 

Rupture of fractal (flocculated) aggregates of polystyrene latices in simple shear flow and converging flow was studied by Sonntag and Russel (1986, 1987b). For simple shear flow and low electrolyte concentrations, the critical fragmentation number decreases sharply with agglomerate radius (R) as... 

For fractal agglomerates, the critical fragmentation number is inversely proportional to its volume (R/a)3... 

Baveye, P., Boast, C. W., Gaspard, S., and Tarquis, A. M. (2008). Introduction to fractal geometry, fragmentation processes and multifractal measures Theory and operational aspects of their application to natural systems In Bio-Physical Chemistry of Fractal Structures and Process in Environmental Systems, Senesi, N., and Wilkinson, K., eds. IUPAC Series on Analytical and Physical Chemistry of Environmental Systems. Vol. 11, John Wiley Sons, Chichester, pp. 11-67. 

Mizoue LS, Bazan JF, Johnson EC, Handel TM (1999) Solution structure and dynamics of the CX3C chemokine domain of fractal-kine and its interaction with an N-terminal fragment of CX3CR1. Biochemistry 38 1402-1414. 

The concept of fractal geometry was first introduced by Mandelbrot and it refers to a rough or fragmented geometric shape that is composed of many smaller copies that have the same shape but different sizes of the whole figure and fractal dimension is a statistical tool to measure how the fractal object rills the space (44). 

Conductivity. Let a(/j be the conductivity of a fragment of the fractal structure of dimension /, where Iq < l < E,. Because of the self-similarity of the structure, the ratio of conductivities on different scales l and / is defined only by the ratio of the scales ... 

Eghball, B., L.N. Mielke, G.A. Calvo, and W.W. Wielhelm. 1993a. Fractal description of soil fragmentation for various tillage methods and crop sequences. Soil Sci. Soc. Am. J. 57 1337-1341. 

---