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We consider the application of fractal concepts to polymer statistics and to anomalous transport in randomly porous media. It is found that answers to interesting physics questions can be expressed in terms of several new fractal dimensions (in addition to “the” fractal dimensiondf): (1)dfBB, the fractal dimension of the backbone, arises in connection with electric current flow, (2)dred, the fractal dimension of the singly connected bonds in the backbone, arises in connection with its equivalence to the thermal scaling power, (3)dE, the fractal dimension of the of the elastic backbone, (4)du, the fractal dimension of the unscreened perimeter, arises in connection with the viscosity singularity at the gelation threshold, (5)dmin the fractal dimension of the minimum path (or “chemical distance”) between two sites, arises in co-nnection with the Aharony-Stauffer conjecture, (6)dw, the fractal dimension of a random walk, (7)dG, the fractal dimension of growth sites that arise as a random walk creates a cluster. Relations among these fractal dimensions are discussed, some of which can be proved and others of which are conjectures whose validity has been established only in certain limiting cases.

Application of fractal concepts to polymer statistics and to anomalous transport in randomly porous media