# The quest for infinite paths

### 5 Dec 2022

ETH Zurich interview with our member Barbara Dembin:

"How does water seep through porous rock? Investigating this question with a mathematical model was the starting point for her research. The mathematician is generating new insights in what is known as percolation theory.

Barbara Dembin is standing in front of the blackboard in her office in the ETH Main Building, drawing a circle with bumps and dents with chalk – the outline of a rock. “How does water permeate the rock from the outside?” she asks while sketching a few thin lines that lead into the circle in different ways. To answer this question, she explains, one has to introduce a parameter. Dembin draws a “p” on the board. The p parameter indicates the density of the holes in the rock, i.e. the average number of holes in a small piece of rock. If p reaches a certain threshold, the rock is porous and thus permeable to water...."

Text and image ETH Zurich website

Image: ETH and Alessandro Della Bella