Relation between critical exponent of the conductivity and the morphological exponents of percolation theory.

A central unsolved problem in percolation theory over the past five decades has been whether there is a direct relationship between the critical exponents that characterize the power-law behavior of the transport properties near the percolation threshold, particularly the effective electrical conductivity σ_{e}, and the exponents that describe the morphology of percolation clusters. The problem is also relevant to the relation between the static exponents of percolation clusters and the critical dynamics of spin waves in dilute ferromagnets, the elasticity of gels and composite solids, hopping conductivity in semiconductors, solute transport in porous media, and many others. We propose an approach to address the problem by showing that the contributions to σ_{e} can be decomposed into several groups representing the structure of percolation networks, including their mass and tortuosity, as well as constrictivity that describes the fluctuations in the driving potential gradient along the transport paths.

Color-gradient-based phase-field equation for multiphase flow.

In this paper, the underlying problem with the color-gradient (CG) method in handling density-contrast fluids is explored. It is shown that the CG method is not fluid invariant. Based on nondimensionalizing the CG method, a phase-field interface-capturing model is proposed which tackles the difficulty of handling density-contrast fluids.

Shuffle & untangle: novel untangle methods for solving the tanglegram layout problem.

Motivation: A tanglegram is a plot of two-tree-like diagrams, one facing the other, and having their labels connected by inter-tree edges. These two trees, which could be both phylogenetic trees and dendrograms stemming from hierarchical clusterings, have thus identically labelled leaves but different topologies. As a result, the inter-tree edges of a tanglegram can be intricately tangled and difficult to be analysed and explained by human readers.

Geometrically derived efficiency of slow immiscible displacement in porous media.

The efficiency of a displacement is the fraction of applied work over the change in free energy. This displacement efficiency is essential for linking wettability to applied work during displacement processes. We quantify the efficiency of slow immiscible displacements in porous media from pore space geometry.

Re-examining Archie's law: Conductance description by tortuosity and constriction.

In this article we investigate the electrical conductance of an insulating porous medium (e.g., a sedimentary rock) filled with an electrolyte (e.