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SPECIAL SECTION: FRACTALS

Modeling Dynamic Fragmentation of Soil

^a Soil Science Dep., Rothamsted Research, Harpenden, Hertfordshire, AL5 2JQ, UK
^b Dpto. de Matemática Aplicada a la Ingeniería Agronómica, E.T.S. Ingenieros Agrónomos, Univ. Politécnica de Madrid, Madrid, Spain, and CEIGRAM, U.P.M., Spain
^* Corresponding author (nigel.bird{at}bbsrc.ac.uk).

Received 25 February 2008.

Soil fragmentation is a critical component in determining the structure of soil at any instant in time. Modeling and describing soil fragmentation consequently occupies an important niche in soil research. Recent attention has focused on a simple deterministic model of soil fragmentation that encompasses the notion of scale invariance and yields characteristic power-law or fractal size distributions. This model lacks a temporal component, which means that its applicability to a host of real scenarios, involving progressive comminution of soil in time, appears restricted. Our purpose in this study was to generalize this deterministic approach to modeling fragmentation by explicitly including time and by relaxing the requirement for scale invariance. We examined the consequences of these simple modifications in terms of the evolving fragment size distributions. We investigated the development of three different outcomes. The first is a skewed unimodal distribution of the logarithm of fragment size. The second is a unimodal distribution well approximated by the lognormal distribution, and the third is a local power-law distribution. The outcome was dependent on the choice of how fragmentation was modeled as a function of scale. We concluded that power-law distributions should be regarded as the exception rather than the rule in a temporal fragmentation of soil and that we should expect to find power-law scaling locally rather than across the full range of fragment sizes.

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