Topological characteristics of model gels

The Euler characteristic of an object is a topological invariant determined by the number of handles and holes that it contains. Here, we use the Euler characteristic to profile the topology of model three-dimensional gel-forming fluids as a function of increasing length scale. These profiles act as a 'topological fingerprint' of the structure, and can be interpreted in terms of three types of topological events. As model fluids we have considered a system of dipolar dumbbells, and suspensions of adhesive hard spheres with isotropic and patchy interactions in turn. The correlation between the percolation threshold and the length scale on which the Euler characteristic passes through zero is examined and found to be system-dependent. A scheme for the efficient calculation of the Euler characteristic with and without periodic boundary conditions is described.