Numerical Simulation and Role of Noise in the Cahn-Hilliard-Cook Equation below the Critical Dimension

K.A. Hawick (New Zealand)


numerical methods; simulation; model development; statistical modelling; Cahn Hilliard Cook equation; stochastic noise.


Introducing stochastic or thermal noise into partial differ ential equations that would otherwise be deterministic is a useful technique for the analysis of ensemble simula tions. It can also aid the unfreezing of structural growth barriers that occur in spatial growth systems. This ar ticle presents some modelling experiments using Cook’s noise term in the Cahn-Hilliard-Cook equation simulated on multi-dimensional spatial meshes. We show that below the critical dimension noise is actually necessary to enable long-term spatial growth behaviours that are sufficiently driven by surface tension effects in higher dimensions. We also discuss numerical methods for the study using finite differecing techniques.

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