Disorder, Memory and Avalanches in Sandpiles

We construct a cellular-automaton model of a sandpile with unquenched disorder. This models the behaviour of a real sandpile in which the structure is disordered and grain rearrangements cause the structure to change with time. We find that the avalanches retain a memory of the evolving disorder and do not exhibit Self-Organised Criticality. SOC is retrieved in the limit of no disorder. We construct a phase diagram, for the scaling properties, which is parametrised in terms of disorder and its rate of change and we provide a framework for the interpretation of recent theory and experiments.