We investigate the role of disorder on the fracturing process of heterogeneous materials by means of a two-dimensional fuse network model. Our results in the extreme disorder limit reveal that the backbone of the fracture at collapse, namely, the subset of the largest fracture that effectively halts the global current, has a fractal dimension of 1.22 ± 0.01. This exponent value is compatible wi...

We propose a new Ising spin glass model on Z of Edwards-Anderson type, but with highly disordered coupling magnitudes, in which a greedy algorithm for producing ground states is exact. We find that the procedure for determining (infinite volume) ground states for this model can be related to invasion percolation with the number of ground states identified as 2 , where N = N (d) is the number of...

Using digitized images of the three-dimensional, branching structures for root systems of bean seedlings, together with analytical and numerical methods that map a common susceptible-infected-recovered ('SIR') epidemiological model onto the bond percolation problem, we show how the spatially correlated branching structures of plant roots affect transmission efficiencies, and hence the invasion ...

Direct disposal of liquid CO2 on the ocean floor is one of the approaches considered for sequestering CO2 in order to reduce its concentration in the atmosphere. At oceanic depths deeper than approximately 3000 m, liquid CO2 density is higher than the density of seawater and CO2 is expected to sink and form a pool at the ocean floor. In addition to chemical reactions between CO2 and seawater to...

The sapwood fibers in green softwood are normally filled – or nearly filled – with free water. This water forms a continuous phase through the narrow bordered pits between fiber lumens. In a drying process water evaporates from the menisci formed at these narrow throats and initially located close to the surface of the wood. As the amount of free water decreases in this way, a retraction of the...

Stochastic models that account for a wide range of pore-scale e€ects are discussed in the context of two-phase, immiscible displacement problems in natural porous media. We focus on migration of dense, nonaqueous phase liquids (DNAPLs) through watersaturated geological materials. DNAPL movement is governed by buoyancy, capillary, and viscous forces, as well as by the details of the porous mediu...

We present an advanced algorithm for the determination of watershed lines on Digital Elevation Models (DEMs), which is based on the iterative application of Invasion Percolation (IIP) . The main advantage of our method over previosly proposed ones is that it has a sub-linear time-complexity. This enables us to process systems comprised of up to 10 sites in a few cpu seconds. Using our algorithm...

The drying of liquid-saturated porous media is typically approached using macroscopic continuum models involving phenomenological coecients. Insight on these coecients can be obtained by a more fundamental study at the poreand pore-network levels. In this paper, we present a model based on a pore-network representation of porous media that accounts for various processes at the pore-scale. The...

Employing highly efficient algorithms for simulating invasion percolation (IP) with trapping, we obtain precise estimates for the fractal dimensions of the sample-spanning cluster, the backbone, and the minimal path in a variety of two-dimensional lattices. The results indicate that these quantities are nonuniversal and vary with the coordination number Z of the lattices. In particular, while t...