Noteworthy fractal features and transport properties of Cantor tartans

Balankin A. S., Khalili Golmankhaneh A., Patiño-Ortiz J., Patiño-Ortiz M.

Physics Letters, Section A: General, Atomic and Solid State Physics, cilt.382, sa.23, ss.1534-1539, 2018 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 382 Sayı: 23
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1016/j.physleta.2018.04.011
  • Dergi Adı: Physics Letters, Section A: General, Atomic and Solid State Physics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1534-1539
  • Anahtar Kelimeler: Anomalous diffusion, Cantor tartan, Fractal networks, Mass and momentum transport, Random walks, Spectral dimension
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

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