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4
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0000668370
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Y. Park, A. B. Harris, and T. Lubensky [, ] studied the voltage distribution problem using an epsilon-expansion field-theory approach. They found multifractal behavior, but since the technique is complicated the origin of it is not clear.
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(1987)
Phys. Rev. B
, vol.35
, pp. 5048
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8
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0000353472
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Diffusive motion on a fractal;Gnm(t)
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It is also relevant to several other problems of interest such as quantum localization [, 4, 1355, ], or self-avoiding walks on fractals , A. B. Harris, A. Aharony, Europhys. Lett., A. Aharony, A. B. Harris, J. Stat. Phys., 54, 1091
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(1984)
Physical Review A
, vol.32
, pp. 2324
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Guyer, R.A.1
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9
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84926802521
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for a review see Ref. 10.
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10
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84926802520
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Linear fractals are topologically linear paths consisting of consecutively ordered segments. Although, when viewed geometrically, the path can intersect itself, it can still be defined uniquely as a linear chain of ordered segments. Special cases of linear fractals are random walks and self-avoiding walks in d dimensions (see also Ref. 9). Percolation clusters occur, e.g., in random resistor networks at the critical resistor concentration. In contrast to linear fractal structures, percolation clusters have loops and dangling ends on all length scales [see, e.g., D. Stauffer, Introduction to Percolation Theory (Taylor and Francis, London, 1985)].
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11
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45949115280
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The multifractal features described by (1) and (2) are distinct from the multifractal behavior found in kinetic aggregation or voltage drops in percolation, where the scaling parameter is the size of the system and τ ( q ) approaches a straight line for q -> inf. The scaling parameter here is langle P ( r, t ) rangle, which is similar to the study of intermittency in chaotic dynamical systems [, ]. Using the f ( α ) formalism it can be shown that in our case of diffusion on random fractals αmin= 0 and αmax= inf. The f ( α ) spectrum changes from - inf at α = 0 to 1 for α -> inf. The crossover from negative to positive values of f ( α ) has an interesting interpretation that will be discussed elsewhere.
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(1987)
Phys. Rep.
, vol.156
, pp. 147
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Paladin, G.1
Vulpiani, A.2
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12
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84926802519
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The chemical distance l between two sites on the fractal is the shortest path on the structure connecting them;
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13
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0000640467
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the chemical dimension dl characterizes how the mass scales with l, M app ldl P ( l, t ) is the probability to find the walker in chemical (topological) distance l from the origin, for a given configuration see, e.g.
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(1984)
J. Phys. A
, vol.17
, pp. L427
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Havlin, S.1
Nossal, R.2
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19
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84926846577
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Previous numerical work on random walks in percolation clusters (see Ref. 10 and references therein) were slightly larger than those predicted by (9) and (11). The extensive simulations on larger systems presented here confirm these relations for random walks in percolation clusters in d = 2.
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