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Study of Diffusion on a Deterministic Fractal
Author(s) -
Dasgupta R.,
Ballabh T. K.,
Tarafdar S.
Publication year - 1994
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221810205
Subject(s) - sierpinski triangle , fractal , random walk , exponent , statistical physics , random walker algorithm , mathematics , diffusion , square (algebra) , anomalous diffusion , physics , mathematical analysis , geometry , statistics , thermodynamics , computer science , innovation diffusion , linguistics , philosophy , knowledge management
Fractal systems exhibit anomalous diffusion where the mean square distance covered in a random walk (RW) is related to time t as 〈 r 2 〉 ∼ t 2/dw with d w ≠ 2. The presence of a bias along any direction in fractal systems gives rise to competing effects ‐ enhanced diffusion as well as trapping at dead ends. A random walk on a Vicsek fractal (VF) is studied. The same exponent d w is obtained from a similar vibrating mass‐spring system. Introducing a bias along the positive Y‐direction in RWs, the competing effects are also observed. Results are compared with another well‐studied deterministic fractal, the Sierpinski gasket (SG).