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Explore the fascinating world of elastic frames and network rigidity in this comprehensive lecture by Professor Tom Lubensky. Delve into the mathematical principles behind the stability of various structures, from architectural designs to protein networks. Learn about the critical rigidity threshold, its impact on elastic properties, and the unique characteristics of networks near their instability limit. Examine the behavior of periodic and diluted periodic lattices, focusing on zero modes, states of self-stress, and surface phonons under different boundary conditions. Discover the applications of these concepts to diverse fields, including crystalline solids, granular matter, and semi-flexible polymer networks. Gain insights into the relationship between coordination number and network stability, and understand the emergence of power-law scaling and diverging length scales near the isostatic point.
