The aim of this paper is to extend the well-known asymptotic shape result for first-passage percolation on Z to first-passage percolation on a random environment given by the infinite cluster of a supercritical Bernoulli percolation model. We prove the convergence of the renormalized set of wet vertices to a deterministic shape that does not depend on the realization of the infinite cluster. As...

A theory is presented of how orienting fields and steric interactions conspire against the formation of a percolating network of, in some sense, connected elongated colloidal particles in fluid dispersions. We find that the network that forms above a critical loading breaks up again at higher loadings due to interaction-induced enhancement of the particle alignment. Upon approach of the percola...

We investigate the percolation thresholds of both random and invasion percolation in two and three dimensions on elongated lattices; lattices with a geometry of Ld−1 × nL in d dimensions, where n denotes the aspect ratio of the lattice. Scaling laws for the threshold and spanning cluster density for random percolation are derived and simulation confirms the behaviour. A direct relationship betw...

The study of fluid flow process through porous media has attracted much attention in geographical information systems due to its importance in petroleum and environmental applications, such as: groundwater assessment, soil hydrology and pollution analysis and oil exploration and recovery. In this work we propose an interactive tool, named VisFluid, that uses a simulation engine based on dynamic...

Simultaneous capillary dominated displacement of the wetting and non-wetting phases are processes of interest in many disciplines including modeling of the penetration of polluting liquids in hydrology or the secondary migration in petroleum reservoir engineering. Percolation models and in particular invasion percolation is well suited to characterize the slow immiscible displaceme...

We describe a robust method for determining morphological properties of filamentous biopolymer networks, such as collagen or other connective tissue matrices, from confocal microscopy image stacks. Morphological properties including pore size distributions and percolation thresholds are important for transport processes, e.g., particle diffusion or cell migration through the extracellular matri...

Percolation is a concept widely used in many fields of research and refers to the propagation of substances through porous media (e.g., coffee filtering), or the behaviour of complex networks (e.g., spreading of diseases). Percolation theory asserts that most percolative processes are universal, that is, the emergent powerlaws only depend on the general, statistical features of the macroscopic ...

Tortuosity (T) is a parameter describing an average elongation of fluid streamlines in a porous medium as compared to free flow. In this paper several methods of calculating this quantity from lengths of individual streamlines are compared and their weak and strong features are discussed. An alternative method is proposed, which enables one to calculate T directly from the fluid velocity field,...