Information dimension, multifractals

Let us consider now this h q)othesis experimental confirmations and dimensions and d estimation methods in reference to amorphous glassy pol5mers multifractal structure. As it is known [82], the informational dimension characterizes behavior Shennone informational entropy 7(e) ... 

Since the polymers structure is multifractal [53], then, following to Williford [42], the fracture surface can be considered as the first subfractal, having dimension d (information dimension, see the Eq. (4.49)) [48]. In this case within the fiiameworks of the indicated above formalism [42] a=f, where/is dimension of singularities a, equal to [47] ... 

In the general case polymers structure is multifractal, for behavior description of which in deformation process in principle its three dimensions knowledge is enough fractal (Hausdorff) dimension d informational one d and correlation one d [82]. Each from the indicated dimension describes multifractal definite properties change and these dimensions combined application allows to obtain more or less complete picture of yielding process [73]. 

FIGURE 4.21 The temperature dependences of correlation J (1), informational (2) and Hausdorff d (3) dimensions of PC multifractal structure [73]. 

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See also in sourсe #XX -- [ , ]

See also in sourсe #XX -- [ , ]

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