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A highly polydisperse granular gas is modeled by a continuous distribution ofparticle sizes, a, giving rise to a corresponding continuous temperatureprofile, T(a), which we compute approximately, generalizing previous resultsfor binary or multicomponent mixtures. If the system is driven, it evolvestowards a stationary temperature profile, which is discussed for severaldriving mechanisms in dependence on the variance of the size distribution. Fora uniform distribution of sizes, the stationary temperature profile isnonuniform with either hot small particles (constant force driving) or hotlarge particles (constant velocity or constant energy driving). Polydispersityalways gives rise to non-Gaussian velocity distributions. Depending on thedriving mechanism the tails can be either overpopulated or underpopulated ascompared to the molecular gas. The deviations are mainly due to smallparticles. In the case of free cooling the decay rate depends continuously onparticle size, while all partial temperatures decay according to Haff's law.The analytical results are supported by event driven simulations for a large,but discrete number of species.

Partitioning of energy in highly polydisperse granular gases