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Rigidity And Fluidity In Living And Nonliving Matter, Jorge Hernan Lopez

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Many of the standard equilibrium statistical mechanics techniques do not readily apply to non-equilibrium phase transitions such as the fluid-to-disordered solid transition found in repulsive particulate systems. Examples of repulsive particulate systems are sand grains and colloids. The first part of this thesis contributes to methods beyond equilibrium statistical mechanics to ultimately understand the nature of the fluid-to-disordered solid transition, or jamming, from a microscopic basis.

In Chapter 2 we revisit the concept of minimal rigidity as applied to frictionless, repulsive soft sphere packings in two dimensions with the

introduction of the jamming graph. Minimal rigidity is a purely combinatorial …