The concept of tortuosity is used to characterize the structure of porous media, to estimate
their electrical and hydraulic conductivity, and to study the travel time and length for tracer …

We review and discuss recent progress in modelling non-linear and non-local transport
processes in heterogeneous media. The non-locality that we consider is caused by long …

Fluid–fluid displacement in porous media has been viewed through the lens of Lenormand's
phase diagram since the late 1980s. This diagram suggests that the character of the flow is …

We study the optimal distance in networks, ℓ opt, defined as the length of the path
minimizing the total weight, in the presence of disorder. Disorder is introduced by assigning …

When biological populations expand into new territory, the evolutionary outcomes can be
strongly influenced by genetic drift, the random fluctuations in allele frequencies. Meanwhile …

We study traveling time and traveling length for tracer dispersion in two-dimensional bond
percolation, modeling flow by tracer particles driven by a pressure difference between two …

Employing highly efficient algorithms for simulating invasion percolation (IP), whose
execution time scales as O [Mlog (M)] or better for a cluster of M sites, and for determining …

What is the scaling limit of diffusion-limited aggregation (DLA) in the plane? This is an old
and famously difficult question. One can generalize the question in two ways: first, one may …

Tortuosity is a property of porous media that is invoked and used in the literature on
hydrology, soil science, physics, and engineering. It has been defined in a variety of ways …

In this book, the authors bring together basic ideas from fracture mechanics and statistical
physics, classical theories, simulation and experimental results to make the statistical …