Crack patterns formed due to desiccation of clay or similar materials show distinctive reproducible patterns. If one measures the cumulative area Acum covered by the cracks with widths ≥Wmin, then Acum plotted against Wmin shows a typical reproducible shape. In a log–log plot, this curve has two roughly linear regions with different slopes. For a polypropylene (PP) substrate, there is a sharp change from a nearly horizontal line to a very steep line, whereas for a glass substrate, which is smoother, there is a gradual changeover between the two regions. We propose a simple one-dimensional spring chain model, in which reducing the natural length of the springs corresponds to the desiccation process. Springs may break, or slip against the substrate to accommodate strain beyond a specified threshold. The model successfully reproduces the successive stages of crack formation and behaviour of the cumulative area curve, as observed in experiments. The difference in the qualitative nature of the patterns on smooth and rougher substrates is also obtained.

We investigate the flux of particles in a smooth single-file channel where particles cannot cross each other as well as in wider channels of varying cross section where particles execute normal diffusion. All the channels are connected to an infinite reservoir at one end and the flux of particles is measured at the other open end. We perform random walk Monte Carlo simulation using lattice model. The flux decreases monotonically as the channel cross section is increased from single-file channel to wider channel and finally reaches a constant value for a sufficiently wide channel. The observation of enhanced flux in single-file channel as compared to a wider channel can be tested for efficient separation of particles through smooth nanochannels.

We present a cellular automaton (CA) model of particles in a single-file motion with free particle exchange at the boundaries of a one-dimensional channel connected to two infinite reservoirs in order to study the self-transmission of particles with excluded mutual passage. The parallel, local and homogeneous rule sets of the CA algorithm consider two different interactions of varying strength between particles, without any specific particle-channel interaction. CA model results suggest that one hallmark of single-file motion is the conduction bursts at a particular time scale, which have thus far only been discovered for hydrogen bond networked water translocation. The cumulative transport probabilities of particles through single-file channels of different length follow a single profile, which can be obtained through proper scaling of time. The universal features of our results suggest new experiments in single-file channel with fluids other than water.

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