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RHex is a hexapod with compliant legs and only six actuated degrees of freedom. Its ability to traverse highly fractured and unstable terrain, as well ascend and descend a particular flight of stairs has already been documented. In this paper, we describe an open loop controller that enables our small robot (Length: 51 cm, Width: 20 cm, Height: 12.7 cm. Leg(More)
No tribute to the legacy of Stan Ulam would be complete without a discussion of " nonlinear science, " a growing collection of interdisciplinary studies that in the past two decades has excited and challenged researchers from nearly every discipline of the natural sciences, engineering, and mathematics. Through his own research Stan played a major role in(More)
n solid-state physics, the phenomenon of localization is usually perceived as arising from extrinsic disorder that breaks the discrete translational invariance of the perfect crystal lattice. Familiar examples include the localized vibrational phonon modes around impurities or defects (such as atomic vacancies or interstitial atoms) in crystals and Anderson(More)
A continuum model of a Peierls-dimerized chain, as described generally by Brazovskii and discussed for the case of polyacetylene by Takayama, Lin-Liu and Maki (TLM), is considered. The continuum (Bogliubov-de Gennes) equations arising in this model of interacting electrons and phonons are shown to be equivalent to the static, semiclassical equations for a(More)
We develop an asymptotically exact renormalization-group approach that treats electron-electron and electron-phonon interactions on an equal footing. The approach allows an unbiased study of the instabilities of Fermi liquids without the assumption of a broken symmetry. We apply our method to the problem of strongly coupled superconductors and find the(More)
We report three surprising results regarding the nature of the spatial broken symmetries in the two-dimensional ͑2D͒, quarter-filled band with strong electron-electron interactions that provides a microscopic model of the 2:1 cationic organic charge-transfer solids ͑CTS's͒. First, in direct contradiction to the predictions of one-electron theory, we find a(More)