TY - JOUR
T1 - Noteworthy fractal features and transport properties of Cantor tartans
AU - Balankin, Alexander S.
AU - Golmankhaneh, Alireza K.
AU - Patiño-Ortiz, Julián
AU - Patiño-Ortiz, Miguel
N1 - Publisher Copyright:
© 2018 Elsevier B.V.
PY - 2018/6/12
Y1 - 2018/6/12
N2 - This Letter is focused on the impact of fractal topology on the transport processes governed by different kinds of random walks on Cantor tartans. We establish that the spectral dimension of the infinitely ramified Cantor tartan ds is equal to its fractal (self-similarity) dimension D. Consequently, the random walk on the Cantor tartan leads to a normal diffusion. On the other hand, the fractal geometry of Cantor tartans allows for a natural definition of power-law distributions of the waiting times and step lengths of random walkers. These distributions are Lévy stable if D>1.5. Accordingly, we found that the random walk with rests leads to sub-diffusion, whereas the Lévy walk leads to ballistic diffusion. The Lévy walk with rests leads to super-diffusion, if D>3, or sub-diffusion, if 1.5<D<3.
AB - This Letter is focused on the impact of fractal topology on the transport processes governed by different kinds of random walks on Cantor tartans. We establish that the spectral dimension of the infinitely ramified Cantor tartan ds is equal to its fractal (self-similarity) dimension D. Consequently, the random walk on the Cantor tartan leads to a normal diffusion. On the other hand, the fractal geometry of Cantor tartans allows for a natural definition of power-law distributions of the waiting times and step lengths of random walkers. These distributions are Lévy stable if D>1.5. Accordingly, we found that the random walk with rests leads to sub-diffusion, whereas the Lévy walk leads to ballistic diffusion. The Lévy walk with rests leads to super-diffusion, if D>3, or sub-diffusion, if 1.5<D<3.
KW - Anomalous diffusion
KW - Cantor tartan
KW - Fractal networks
KW - Mass and momentum transport
KW - Random walks
KW - Spectral dimension
UR - http://www.scopus.com/inward/record.url?scp=85045124416&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2018.04.011
DO - 10.1016/j.physleta.2018.04.011
M3 - Artículo
SN - 0375-9601
VL - 382
SP - 1534
EP - 1539
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 23
ER -