Abstract
The ant in the labyrinth problem posed by de Gennes in 1976 concerned the description of the random movement of an entity (the ant) in a disordered system (the labyrinth) [8] and was a metaphor for the general problem of transport in disordered media. The general physical problem was to represent the evolution of conduction electrons in amorphous materials, phase dislocations in polymer gels, and myriad other phenomena. On the other hand, the ant as metaphor, like every other localized quantity in physics, has its corresponding nonlocal, wavelike aspect. Material properties, such as the distribution of grain sizes in polycrystalhne materials, the degree of homogeneity, the existence of microscopic cracks, inclusions, twin boundaries, and dislocations, all affect fracture micromechanics and wave propagation. To describe the motion of this generalized ant through such disordered, but scaling, materials we change de Gennes’ image to that of an ant in a gurge, that is, an ant in a kind of turbulent flow field. In terms of this modified image we construct an equation that in one limit models fractional diffusion and in another limit models fractional wave propagation. This new equation is the fractional generalization of the telegrapher’s equation. But in addition to these physical processes we also use this metaphor to describe the influence of scaling on the observables in other complex phenomena as well.1
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West, B.J., Bologna, M., Grigolini, P. (2003). The Ant in the Gurge Metaphor. In: Physics of Fractal Operators. Institute for Nonlinear Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21746-8_9
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DOI: https://doi.org/10.1007/978-0-387-21746-8_9
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