Hybrid ramified Sierpinski carpet: percolation transition, critical exponents, and force field

A.N. Herega^a, N.G. Drik^b, A.P. Ugol’nikov^c
^aOdessa State Academy of Building and Architecture, Didrikhsona st. 4, Odessa, 65029, Ukraine
^bMechnikov Odessa National University, Dvoryanskaya st. 2, Odessa, 65026, Ukraine
^cThe Odessa State Academy of Refrigeration, Dvoryanskaya st. 1/3, Odessa, 65082, Ukraine

This methodological note introduces the concept of and calculates percolation transition characteristics for a Sierpinski carpet with hybrid (finite—infinite) ramification. Recurrence formulas for calculating the force fields of Sierpinski prefractals of an arbitrary generation are obtained. The possibility of using the obtained results in the model of oscillatory interacting different-scale inner boundaries of a heterogeneous material is discussed.

PACS: 64.60.ae, 64.60.ah, 64.60.al, 64.60.−i (all)
DOI: 10.3367/UFNe.0182.201205f.0555
URL: https://ufn.ru/en/articles/2012/5/f/
Citation: Herega A N, Drik N G, Ugol’nikov A P "Hybrid ramified Sierpinski carpet: percolation transition, critical exponents, and force field" Phys. Usp. 55 519–521 (2012)

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Received: 1st, August 2011, accepted: 2nd, August 2011

Оригинал: Герега А Н, Дрик Н Г, Угольников А П «Ковёр Серпинского с гибридной разветвлённостью: перколяционный переход, критические показатели, силовое поле» УФН 182 555–557 (2012); DOI: 10.3367/UFNr.0182.201205f.0555