Random-walk simulation of the solvability theory for the Saffman-Taylor problem

We test the predictions of the solvability theory in the Saffman-Taylor problem by a random-walk simulation. By a suitable modification of the surface tension in accordance with the solvability theory, we observe a dynamically stable cusp to develop on the finger profile leading to a substantial reduction in a finger width. Identifying this cusp with that originating from the solvability theory, we find an excellent agreement between the simulation results and the solvability theory.