TY - JOUR
T1 - The topological Hausdorff dimension and transport properties of Sierpiński carpets
AU - Balankin, Alexander S.
N1 - Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2017/9/12
Y1 - 2017/9/12
N2 - In this Letter, the analytical expression of topological Hausdorff dimension DtH is derived for some kinds of infinitely ramified Sierpiński carpets. Furthermore, we deduce that the Hausdorff dimension of the union of all self-avoiding paths admitted on the infinitely ramified Sierpiński carpet has the Hausdorff dimension DHsa=DtH. We also put forward a phenomenological relation for the fractal dimension of the random walk on the infinitely ramified Sierpiński carpet. The effects of fractal attributes on the transport properties are highlighted. Possible applications of the developed tools are briefly outlined.
AB - In this Letter, the analytical expression of topological Hausdorff dimension DtH is derived for some kinds of infinitely ramified Sierpiński carpets. Furthermore, we deduce that the Hausdorff dimension of the union of all self-avoiding paths admitted on the infinitely ramified Sierpiński carpet has the Hausdorff dimension DHsa=DtH. We also put forward a phenomenological relation for the fractal dimension of the random walk on the infinitely ramified Sierpiński carpet. The effects of fractal attributes on the transport properties are highlighted. Possible applications of the developed tools are briefly outlined.
KW - Fluid momentum diffusion
KW - Ramification
KW - Random walk
KW - Sierpiński carpet
KW - Topological Hausdorff dimension
KW - Tortuosity
UR - http://www.scopus.com/inward/record.url?scp=85024502201&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2017.06.049
DO - 10.1016/j.physleta.2017.06.049
M3 - Artículo
AN - SCOPUS:85024502201
SN - 0375-9601
VL - 381
SP - 2801
EP - 2808
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 34
ER -