Optimal percolation of disordered segregated composites

We evaluate the percolation threshold values for a realistic model of continuum segregated systems, where random spherical inclusions forbid the percolating objects, modellized by hard-core spherical particles surrounded by penetrable shells, to occupy large regions inside the composite. We find that the percolation threshold is generally a non-monotonous function of segregation, and that an optimal (i. e., minimum) critical concentration exists well before maximum segregation is reached. We interpret this feature as originating from a competition between reduced available volume effects and enhanced concentrations needed to ensure percolation in the highly segregated regime. The relevance with existing segregated materials is discussed.

Critical values in an anisotropic percolation on $\mathbb{Z}^2$

Hao Xue

In this thesis, we consider an anisotropic finite-range bond percolation model on

\mathbb{Z}^2

. On each horizontal layer

\{(x,i):x\in\mathbb{Z}\}

for

i\in\mathbb{Z}

, we have edges

\langle(x,i),(y,i)\rangle

for

1\leq|x-y|\leq N

with $N\in\mathbb{N ...

EPFL2021

Optimal percolation of disordered segregated composites

THE PHASE TRANSITION FOR PLANAR GAUSSIAN PERCOLATION MODELS WITHOUT FKG

Critical values in an anisotropic percolation on $\mathbb{Z}^2$

THE PHASE TRANSITION FOR PLANAR GAUSSIAN PERCOLATION MODELS WITHOUT FKG

Critical values in an anisotropic percolation on $\mathbb{Z}^2$