350 rub
Journal Nonlinear World №4 for 2012 г.
Article in number:
Determination of fractal dimension of metal dendrites in jelly polymers
Authors:
T.V. Khecalo
Abstract:
The work contains definitions of fractal dimensions of the metal dendrites in jellies of polymers. We studied the influence of different factors (origin of jelly, salt, metal - seeding, shape of the vessel) on the size of fractal dimension. We used water solutions of high molecular substances: starch, gelatin, agar; metal - seeding (zinc, iron), four salts (lead, copper, tin and silver salts); two shapes of vessels (vertical - test tube, radial - Petri dish). It was established that the shape of dendrite depended on the origin of the jelly and the nature of metal-seeding. The fractal dimension was determined by four methods: 1) the method of counting of the number of cells σ × σ needed for the fractal covering, as the function of the step; 2) the method of determination of the number of geometric features, which σ × σ in this growth; 3) the method of determination of square of fractal according to the mass of imaging as the function of magnification factor; 4) the method of determination of square of fractal according to the brightness of imaging as the function of magnification factor. The value of dendrites - fractal dimension corresponds to the literature data of the same objects and are in the interval of 1,00 ≤ Д < 2,0 The dimension depends on the origin of the jelly and the form the vessel. Is this dendrite a true fractal or depends on the origin of jelly, salt, metal-seeding and the form of the vessel. Only the part of dendrites was true, having fractional dimensions. Physic-chemical system «Metal dendrites in polymers - jellies» can be used as a model of fractal object in laboratory practice on physics or colloidal chemistry for students of pharmaceutical specialties in medical universities.
Pages: 243-246
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