Category: Physics

Summary: Measuring how trapping changes the fractal dimension of invasion-percolation clusters and their finite-size corrections.

Invasion percolation builds a growing cluster by repeatedly invading the easiest available site, and in two dimensions trapping changes the universality class of the resulting geometry. This experiment asks how clearly that trapping-versus-no-trapping difference appears at finite lattice sizes and how quickly each case approaches its asymptotic fractal dimension.

The simulation generates clusters on square lattices with and without trapping and estimates the cluster fractal dimension across system size. It then studies the finite-size correction exponent that controls how the measured dimension converges toward its large-system limit.

That is useful because asymptotic dimension values are known much better than their finite-size approach. The result gives a practical map of how quickly the two universality classes separate in finite simulations.

Method: Square-lattice invasion-percolation simulations with and without trapping, followed by finite-size fits of the cluster fractal dimension.

What is measured: Fractal dimension with trapping, fractal dimension without trapping, finite-size correction exponent, and crossover with lattice size.