Large-scale simulations with distributed computing: Asymptotic scaling of ballistic deposition

Abstract

Extensive kinetic Monte Carlo simulations are reported for ballistic deposition (BD) in (1 + 1) dimensions. The large system sizes L observed for the onset of asymptotic scaling (L ≃ 212) explains the widespread discrepancies in previous reports for exponents of BD in one and likely in higher dimensions. The exponents obtained directly from our simulations, α = 0.499 ± 0.004 and β = 0.336 ± 0.004, capture the exact values α = ½ and β = ⅓ for the one-dimensional Kardar-Parisi-Zhang equation. An analysis of our simulations suggests a criterion for identifying the onset of true asymptotic scaling, which enables a more informed evaluation of exponents for BD in higher dimensions. These simulations were made possible by the Simulation through Social Networking project at the Institute for Advanced Studies in Basic Sciences in 2007, which was re-launched in November 2010.