Invasion percolation: new algorithms and universality classes

Sheppard, Adrian; Knackstedt, Mark; Pinczewski, W.V.; Sahimi, Muhammad

doi:10.1088/0305-4470/32/49/101

Cited by 126 publications

(146 citation statements)

References 24 publications

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“…The double logarithmic plot yields a slope of about 3.5 in the long time limit, compatible with the value of h chosen (from Ref. [111]). This slope may exceed experimental values; a realistic comparison with experiment has not yet begun.…”

Section: O M P L E X I T Y 19supporting

confidence: 66%

“…This is a power-law decay in time, and the year 1979 study result for L [78] would give a power of roughly 29, whereas the most recent estimates (which are claimed to be most accurate [111]) are consistent with a power 23.64. Note that simulations of Dr. Robert Ewing (private communication) appear to give an even larger value of D with associated power 23.2.…”

Section: O M P L E X I T Y 19mentioning

confidence: 80%

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Relevance of percolation theory to power‐law behavior of dynamic processes including transport in disordered media

Hunt

2009

Complexity

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P ower-law behavior seems ubiquitous in nature as well as in human endeavors. Flood statistics [1][2][3][4][5], water storage [6], drainage basin organization [7], relationships between channel dimensions and flow [8], extreme precipitation events [9], wind and weather fluctuations [10,11], stock and commodity markets fluctuations [12,13] , have all been noted to obey various power laws. Many physicists have searched for unifying concepts to explain such ubiquity. Perhaps, however, powerlaw behavior is not quite as universal as thought. Multifractal distributions originating from cascade processes as a related, but somewhat more complex, organizing principle have often been proposed to be the appropriate universal description [33, 34]. Some [35][36][37] have questioned whether a ''class'' of stretched exponential functions might better represent a larger or smaller fraction of the data. In the ac conductivity of disordered insulators, for example, several other frequencydependences [38-40], universal or not, have been suggested. This small sample of alternate ideas need not imply that alternative scenarios are always correct either. But simply because it is often asserted that nature follows power laws does not require such; in most cases the range and quality of data are probably not sufficient to distinguish the subtle differences between the various proposed distributions. But the recognition of the simplicity of the explanation that self-similar geometrical structures [41] could be the basis of so many geophysical manifestations of apparent power laws has certainly provided impetus to the interpretation that a large number of natural phenomena do follow power-law behavior.In the case that one believes that the observed behavior conforms to true power laws, what kind of underlying mechanism should one seek? At least six such unifying concepts, nonlinear dynamics (chaos) [42], self-organized criticality [43], hierarchical dynamics [44], highly optimized tolerance [45], minimum effort

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Section: O M P L E X I T Y 19supporting

confidence: 66%

Section: O M P L E X I T Y 19mentioning

confidence: 80%

Relevance of percolation theory to power‐law behavior of dynamic processes including transport in disordered media

Hunt

2009

Complexity

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“…However, when the medium is highly heterogeneous, e.g., with a wide range of pore sizes, the length L of the optimal paths that provide the most rapid transport across the system is proportional to the system length to a different exponent, D opt , rather than to D min [28,29]. D opt is the so-called optimal paths exponent, and is determined for the heterogeneous limit [30]. The values of the exponents determined by [30] are mostly accurate to five significant figures, but the optimal paths exponent only to three.…”

Section: Percolation Scaling Theory For Solute Transportmentioning

confidence: 99%

“…D opt is the so-called optimal paths exponent, and is determined for the heterogeneous limit [30]. The values of the exponents determined by [30] are mostly accurate to five significant figures, but the optimal paths exponent only to three. The most important distinctions in porous media that affect the exponents D b and D min relate to the connectivity of the paths and the specific percolation conditions: (i) imbibition (wetting) conditions correspond to site invasion percolation with trapping; (ii) drying conditions to invasion percolation with trapping; and (iii) saturated flow to random percolation [20].…”

Section: Percolation Scaling Theory For Solute Transportmentioning

confidence: 99%

A Percolation‐Based Approach to Scaling Infiltration and Evapotranspiration

Hunt

Holtzman

Ghanbarian

2017

Water

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Abstract:Optimal flow paths obtained from percolation theory provide a powerful tool that can be used to characterize properties associated with flow such as soil hydraulic conductivity, as well as other properties influenced by flow connectivity and topology. A recently proposed scaling theory for vegetation growth appeals to the tortuosity of optimal paths from percolation theory to define the spatio-temporal scaling of the root radial extent (or, equivalently, plant height). Root radial extent measures the maximum horizontal distance between a plant shoot and the root tips. We apply here the same scaling relationship to unsteady (horizontal) flow associated with plant transpiration. The pore-scale travel time is generated from the maximum flow rate under saturated conditions and a typical pore size. At the field-scale, the characteristic time is interpreted as the growing season duration, and the characteristic length is derived from the measured evapotranspiration in that period. We show that the two scaling results are equivalent, and they are each in accord with observed vegetation growth limits, as well as with actual limiting transpiration values. While the conceptual approach addresses transpiration, most accessed data are for evapotranspiration. The equivalence of the two scaling approaches suggests that, if horizontal flow is the dominant pathway in plant transpiration, horizontal unsteady flow follows the same scaling relationship as root growth. Then, we propose a corresponding scaling relationship to vertical infiltration, a hypothesis which is amenable to testing using infiltration results of Sharma and co-authors. This alternate treatment of unsteady vertical flow may be an effective alternative to the commonly applied method based on the diffusion of water over a continuum as governed by Richards' equation.

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“…The majority of these studies used the traditional invasion percolation algorithm (e.g., Wilkinson and Willemsen 1983;Sheppard et al 1999). However, as discussed in Ceballos and Prat (2010), the boundary condition of uniform pressure at the inlet used in classical IP simulations can be questioned in the context of PEMFC studies.…”

Section: Literature Reviewmentioning

confidence: 99%

Liquid Invasion from Multiple Inlet Sources and Optimal Gas Access in a Two-Layer Thin Porous Medium

et al. 2016

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. Abstract This study builds upon previous work on single-layer invasion percolation in thin layers to incorporate a second layer with significantly different pore sizes and to study the impact of the resulting water configuration on gas-phase mass transport. We consider a situation where liquid water is injected at the assembly inlet through a series of independent injection points. The challenge is to ensure the transport of the liquid water while maintaining a good diffusive transport within the gas phase. The beneficial impact of the fine layer on the gas diffusion transport is shown. It is further shown that there exists a narrow range of fine layer thicknesses optimizing the gas transport. The results are discussed in relation with the water management issue in polymer electrolyte membrane fuel cells. Additional discussions, of more general interest in the context of thin porous system, are also offered.

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Invasion percolation: new algorithms and universality classes

Cited by 126 publications

References 24 publications

Relevance of percolation theory to power‐law behavior of dynamic processes including transport in disordered media

Relevance of percolation theory to power‐law behavior of dynamic processes including transport in disordered media

A Percolation‐Based Approach to Scaling Infiltration and Evapotranspiration

Liquid Invasion from Multiple Inlet Sources and Optimal Gas Access in a Two-Layer Thin Porous Medium

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