Fractal dimensions physical significance

B) the physical significance of ink bottle theories of mercury intrusion have always been the subject of debate (C) a possible reinterpretation of the data in (A) as fractal data. a. and P are the slopes of particular regions of the resulting curve, which may be interpreted as fractal dimensions. 

As it has been noted above, variation D t) reason is cnring reaction proceeding in fractal space. This process by its physical significance is similar to the formation of clusters with dimension on lattice with dimension [18], In paper [44] it was supposed = D. The relation between and is given by... 

Thus, the stated above results demonstrated the fractal analysis possibilities at polymers local deformation description. In each from the described cases fractal dimension of either element has simple and clear physical significance that allows to obtain both empirical and analytic correlations between different structural levels in polymers and also describe their evolution in polymers deformation and failure processes. 

Let us consider in conclusion the physical significance of stable crack fractal dimension in PASF samples. As it has been shown in Ref [12], the stress concentration coefficient Kg of triangular crack is given by the Eq. (5.10). In Fig. 8.6 the relation between parameters and for PASF sample (solvent - chloroform) is adduced, fi om which linear reduction follows at growth. Thus, the dimension for stable crack has the simple physical significance - it is the value, reciprocal to stress concentration level at crack tip. 

Hence, the stated above results have shown, that the stable crack in PASF samples, obtained from different solvents, can be treated as stochastic fi actal, whose dimension has clear physical significance - its value is reciprocal to stress concentration degree at a crack tip. The value is determined unequivocally by polymer structure fractal dimension and in its turn, influences on PASF samples fracture process parameters [8]. 

The obvious physical significance of local plasticity zone fractal dimension <7 follows from the adduced analysis the greater 8p at fixed the larger strain in the indicated zone (see the Eq. (5.6)) and the larger its fractal dimension [21]. 

Hence, the stated above results shown the conformity of fractional derivatives method and traditional fractal analysis, using Hausdorff dimension d notion. The physical significance of fractional exponent and its determination method were elucidated. The theoretical analysis is given the good quantitative correspondence to experiment [31]. 

It is rather interesting to note that overall the textural fractal dimensions stays virtually the same. The different structural friictal dimensions have physical significance in that the east and west coasts of Great Britain consist of different rock types and are exposed to different formative processes. The west coast, which has a ru ed profile, is made up of more mountainous material and faces into the storms of the Atlantic. 

---