Model for force fluctuations in bead packs

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Abstract
We study theoretically the complex network of forces that is responsible for the static structure and properties of granular materials. We present detailed calculations for a model in which the fluctuations in the force distribution arise because of variations in the contact angles and the constraints imposed by the force balance on each bead of the pile. We compare our results for the force distribution function for this model, including exact results for certain contact angle probability distributions, with numerical simulations of force distributions in random sphere packings. This model reproduces many aspects of the force distribution observed both in experiment and in numerical simulations of sphere packings. Our model is closely related to some that have been studied in the context of self-organized criticality. We present evidence that in the force distribution context, "critical" power-law force distributions occur only when a parameter (hidden in other interpretations) is tuned. Our numerical, mean field, and exact results all indicate that for almost all contact distributions the distribution of forces decays exponentially at large forces.
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