Multiscaling of porous soils as heterogeneous complex networks

Abstract

Abstract. In this paper we present a complex network model based on a heterogeneous preferential attachment scheme to quantify the structure of porous soils. Under this perspective pores are represented by nodes and the space for the flow of fluids between them is represented by links. Pore properties such as position and size are described by fixed states in a metric space, while an affinity function is introduced to bias the attachment probabilities of links according to these properties. We perform an analytical study of the degree distributions in the soil model and show that under reasonable conditions all the model variants yield a multiscaling behavior in the connectivity degrees, leaving a empirically testable signature of heterogeneity in the topology of pore networks. We also show that the power-law scaling in the degree distribution is a robust trait of the soil model and analyze the influence of the parameters on the scaling exponents. We perform a numerical analysis of the soil model for a combination of parameters corresponding to empirical samples with different properties, and show that the simulation results exhibit a good agreement with the analytical predictions.

Quantifying soil complexity using network models of soil porous structure

“…For the evolving soil network model (Santiago et al, 2008, Cárdenas et al, 2010, it was shown that the scaling exponent of the asymptotic degree distribution is within the interval 1 < γ ≤ 3. Comparing the two network models, this finding sets the upper limit to the strength of embedding in the threshold network model m ≤ m c = 2D/(α − 1) indicating that soil pore networks are predominantly disassortative.…”

“…The upper network in Fig. 1 is obtained using the growing network mechanism with extended preferential attachment rule (Santiago et al, 2008), while the lower network in Fig. 1 results from the threshold model (Mooney and Korošak, 2009).…”

“…Here, the non-dimensional parameter m measures the importance of the distance, and the threshold value θ controls the number of links in the network. In the growing network mechanism with extended preferential attachment rule (Santiago et al, 2008), the probability to connect depends on the pore size s i and the distance between the pores i and j to the power of m.…”

“…Specifically two approaches to describe soil pore structure as complex networks of pores have recently been proposed (Mooney and Korošak, 2009;Cárdenas et al, 2010), both emphasizing the role of the spatial embedding of the network. Soil pore structure was described as a complex network of pores using a spatially embedded varying fitness network model (Mooney and Korošak, 2009) or heterogeneous preferential attachment scheme (Santiago et al, 2008). Both approaches reveal the apparent scale-free topology of soils with a power-law distribution P (k) ∝ k −γ of the degrees k of nodes as a consequence of a heterogeneous soil pore size distribution.…”

Scale-free networks embedded in fractal space

“…Two approaches to build complex network models of soilpore organization have recently been developed [42][43][44]. Here we will concentrate on the networks presented in [42] formed by geographical threshold algorithm as described in Sec.…”