Model Selection Based on Bayesian Inference that Uncovers Fundamental Dynamics of Desiccation Crack Patterns

We investigate dynamic properties of fragment size distribution in surface crack patterns observed on a thin layer of drying dense colloidal suspension experimentally and theoretically. The model selection analysis based on Bayesian inference reveals that the time-varying fragment size distribution observed in experiments exhibits a dynamic transition in its functional form from a lognormal distribution to a generalized gamma distribution. In order to explain this dynamic transition theoretically, we construct a statistical model based on an elastic theory that describes the dynamics of the shrinkage of the colloidal suspension owing to the desiccation. The statistical model predicts the existence of a characteristic length scale that determines the crossover of the dynamic transition, and reproduces the functional forms of fragment size distributions observed in experiments quantitatively.