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The Warren Truss Bridge (1848)

Elastic Response and Surface Phonons in Twisted Kagome Lattices Tom C. Lubensky, University of Pennsylvania, DMR 1104707.

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The Warren Truss Bridge (1848)

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  1. Elastic Response and Surface Phonons in Twisted Kagome LatticesTom C. Lubensky, University of Pennsylvania, DMR 1104707 What is that makes structures like the Warren–Truss bridge stable and others such as rectangular array of struts joined with frictionless pins unstable? This is a question that James Clerk Maxwell, who brought us the equations that describe light propagation, first asked in 1857. We have used Maxwell’s ideas to explore the mechanical properties and modes of collapse of twisted and untwisted versions of kagome lattice, which serves as a model of materials such as glasses and granular packings that are just on the verge of mechanical stability. We have shown that the nature of collapse modes depend sensitively on lattice geometry: The untwisted version supports both compression and shear, and the twisted one only shear. Both lattices have zero-energy modes of collapse, but those of the twisted lattice are restricted to the surface and are described by a mathematically sophisticated conformal field theory. Rectangular array of struts and its collapse mode (dotted lines) The Warren Truss Bridge (1848) (b) (a) (c) (d) Different versions of the kagome lattice: (a) untwisted version and (b)-(d) twisted versions. Note that the dimensions of the lattice change equally in all directions as it is twisted. If lattice (d) is stretched along the horizontal axis it will expand (rather than contract as most lattices do) an equal amount in the vertical direction.

  2. PNAS Editorial BoardTom C. Lubensky, University of Pennsylvania, DMR 1104707 For the last two years, I have served as a member of the Editorial Board of the Proceedings of the National Academy of Sciences (PNAS). My primary task has been to edit (including finding appropriate referees for) articles submitted to PNAS that are at the interface between physics and biology. There is a great demand on the part of biological physicists to publish in high-quality journals that biologists read. PNAS is one of the better journals that is read by both physicists and biologists. Biological physics has undergone explosive growth in the last several years, but it is still a science “at the interface,” and it is not an easy task to find appropriate referees, who can judge both physics and biology. I typically spend nearly a full day a week on PNAS related tasks.

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