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We present a theory for the coupled flow of ice, subglacial water and subglacial sediment, which is designed to represent the processes which occur at the bed of an ice sheet. The ice is assumed to flow as a Newtonian viscous fluid, the water can flow between the till and the ice as a thin film, which may thicken to form streams or cavities, and the till is assumed to be transported, either through shearing by the ice, squeezing by pressure gradients in the till, or by fluvial sediment transport processes in streams or cavities. In previous studies, it was shown that the dependence of ice sliding velocity on effective pressure provided a mechanism for the generation of bedforms resembling ribbed moraine, while the dependence of fluvial sediment transport on water film depth provides a mechanism for the generation of bedforms resembling mega-scale glacial lineations. Here, we combine these two processes in a single model, and show that, depending largely on the granulometry of the till, instability can occur in a range of types which range from ribbed moraine through three-dimensional drumlins to mega-scale glacial lineations. [ABSTRACT FROM AUTHOR]

We provide and analyse a model for the growth of bacterial biofilms based on the concept of an extracellular polymeric substance as a polymer solution, whose viscoelastic rheology is described by the classical Flory-Huggins theory. We show that one-dimensional solutions exist, which take the form at large times of travelling waves, and we characterize their form and speed in terms of the describing parameters of the problem. Numerical solutions of the time-dependent problem converge to the travelling wave solutions. [ABSTRACT FROM AUTHOR]