Maxwell's investigations into the stability of Saturn's rings provide one of the earliest analyses of the dynamics of astrophysical discs. Current research in planetary rings extends Maxwell's kinetic theory to treat dense granular gases of particles undergoing moderately frequent inelastic collisions. Rather than disrupting the rings, local instabilities may be responsible for generating their irregular radial structure. Accretion discs around black holes or compact stars consist of a plasma permeated by a tangled magnetic field and may be compared with laboratory fluids through an analogy that connects Maxwell's researches in electromagnetism and viscoelasticity. A common theme in this work is the appearance of a complex fluid with a dynamical constitutive equation relating the stress in the medium to the history of its deformation.
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