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/
Web of Science

000307559000006
Scopus

2-s2.0-84864996679
ADS NASA

2012PhyU...55..519H
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)

BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

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

References (9) Cited by (9) Similar articles (20) ↓

E.N. Rumanov “Critical phenomena far from equilibrium” Phys. Usp. 56 93–102 (2013)
A.A. Katsnel’son, A.I. Olemskoi et al “Self-oscillation processes during the structure relaxation of palladium-metal alloys (Pd—W) saturated with hydrogen” Phys. Usp. 38 317–323 (1995)
V.L. Pokrovsky “Landau and modern physics” Phys. Usp. 52 1169–1176 (2009)
V.P. Makarov, A.A. Rukhadze “Force acting on a substance in an electromagnetic field” Phys. Usp. 52 937–943 (2009)
V.K. Ignatovich “The neutron Berry phase” Phys. Usp. 56 603–604 (2013)
M.Ya. Agre “Multipole expansions in magnetostatics” Phys. Usp. 54 167–180 (2011)
E.D. Trifonov, S.N. Zagoulaev “On the Bose-Einstein condensate partition function for an ideal gas” Phys. Usp. 53 83–90 (2010)
A.L. Buchachenko “Magnetoplasticity and the physics of earthquakes. Can a catastrophe be prevented?” Phys. Usp. 57 92–98 (2014)
G.B. Malykin, V.I. Pozdnyakova “Quadratic Sagnac effect — the influence of the gravitational potential of the Coriolis force on the phase difference between the arms of a rotating Michelson interferometer (an explanation of D C Miller's experimental results 1921—1926)” Phys. Usp. 58 398–406 (2015)
A.V. Shchagin “Fresnel coefficients for parametric X-ray (Cherenkov) radiation” Phys. Usp. 58 819–827 (2015)
A.A. Snarskii “Did Maxwell know about the percolation threshold? (on the fiftieth anniversary оf percolation theory)” Phys. Usp. 50 1239–1242 (2007)
V.F. Khirnyi, A.A. Kozlovskii “Nonlinear effects and domain instability in oxide ceramics” Phys. Usp. 46 657–663 (2003)
O.G. Bakunin “Correlation and percolation properties of turbulent diffusion” Phys. Usp. 46 733–744 (2003)
L.I. Antonov “Macroscopic representation of the magnetization vector field in a magnetic substance” Phys. Usp. 46 1203–1207 (2003)
M.V. Lebedev, O.V. Misochko “On the question of a classical analog of the Fano problem” Phys. Usp. 65 627–640 (2022)
N.I. Shakura, K.A. Postnov et al “Magnetorotational instability in Keplerian disks: a nonlocal approach” Phys. Usp. 66 1262–1276 (2023)
M.A. Demyanov, N.A. Kondratenko “The maximum range of a relativistic throw in a uniform force field” Phys. Usp. 69 (10) (2026)
Ya.M. Blanter, M.I. Kaganov, D.V. Posvyanskii “De Haas-van Alphen effect as a first-order electronic topological transition” Phys. Usp. 38 203–209 (1995)
V.I. Vysotskii, V.I. Vorontsov et al “The Sagnac experiment with X-radiation” Phys. Usp. 37 289–302 (1994)
B.A. Trubnikov “Constrictions in a relativistic pinch with a longitudinal magnetic field” Sov. Phys. Usp. 34 (11) 1018–1020 (1991)

The list is formed automatically.