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Collective Coordinate Control of Density Distributions | | Obioma Uche
; Salvatore Torquato
; Frank Stillinger
; | | Date: |
19 Jun 2006 | | Subject: | Statistical Mechanics; Materials Science | | Abstract: | Real collective density variables $C(oldsymbol{k})$ [c.f. Eq.
ef{Equation3})] in many-particle systems arise from non-linear transformations of particle positions, and determine the structure factor $S(oldsymbol{k})$, where $f k$ denotes the wave vector. Our objective is to prescribe $C({oldsymbol k})$ and then to find many-particle configurations that correspond to such a target $C({f k})$ using a numerical optimization technique. Numerical results reported here extend earlier one- and two-dimensional studies to include three dimensions. In addition, they demonstrate the capacity to control $S(oldsymbol{k})$ in the neighborhood of $ oldsymbol{k} =$ 0. The optimization method employed generates multi-particle configurations for which $S(oldsymbol{k}) propto oldsymbol{k} ^{alpha}$, $ oldsymbol{k} leq K$, and $alpha =$ 1, 2, 4, 6, 8, and 10. The case $alpha =$ 1 is relevant for the Harrison-Zeldovich model of the early universe, for superfluid $^{4}{He}$, and for jammed amorphous sphere packings. The analysis also provides specific examples of interaction potentials whose classical ground state are configurationally degenerate and disordered. | | Source: | arXiv, cond-mat/0606469 | | Services: | Forum | Review | PDF | Favorites | |
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