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Interplay Of Geometry And Mechanics: Disordered Spring Networks And Shape-Changing Cerebella, Mahesh Chandrasekhar Gandikota

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This thesis reports work in three topics - I) isotropic strain-induced rigidity transitions in under-constrained spring networks II) uniaxial strain-induced stiffening transitions in semiflexible networks with area-conserving inclusions and III) non-linearities in the buckling without bending morphogenesis model for growing cerebella. All models are two dimensional and we employ either discrete and continuum models to study these systems.In I), motivated by the rigidity transitions in isotropically strained disordered spring networks, we study rigidity transitions in isotropically strained area-conserving random polygonal loops. We find a crossover transition in these loops. We also provide arguments towards showing convexity as a necessary condition …