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- W2058779981 abstract "Two models, one random the other periodic, are described which exhibit splay rigidity but are not rigid with respect to compression. The random model is based on a periodic lattice of rhombuses whose sides consist of central-force springs, which is perturbed in the following way: rhombuses can have diagonal central force struts with probability y or they can have one of the horizontal springs removed with probability x. For x,yensuremath{ll}1 we are led to consider a long-ranged anisotropic percolation process which is solved exactly on a Cayley tree. We show that for y/x near 2 the compressional rigidity of this system is zero but the Frank elastic constant, K, describing splay rigidity is nonzero. This is the first example of a percolation model for which this phenomenon, suggested earlier, is conclusively established. For y/xensuremath{gtrsim}2 ensuremath{surd}2 the system has nonzero bulk and shear moduli. We also study the excitation spectrum for a periodic model which possesses only splay rigidity and obtain a libron dispersion relation ensuremath{omega}=${c}_{S}$q, where q is the wave vector and ${c}_{S}$ensuremath{sim}(K/ensuremath{rho}${)}^{1/2}$, where ensuremath{rho} is the mass density. These results are generalized to obtain a scaling form for ${c}_{S}$ and the density of states of the random model which is valid when the correlation length for compressional rigidity becomes large." @default.
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- W2058779981 date "1989-10-01" @default.
- W2058779981 modified "2023-09-26" @default.
- W2058779981 title "Central-force models which exhibit a splay-rigid phase" @default.
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- W2058779981 doi "https://doi.org/10.1103/physrevb.40.7256" @default.
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