Collective coordinate control of density distributions

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Obioma U. Uche,¹ Salvatore Torquato,^2,3,4,5 and Frank H. Stillinger²
¹Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544, USA
²Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
³Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA
⁴Program in Applied & Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
⁵Princeton Center for Theoretical Physics, Princeton University, Princeton, New Jersey 08544, USA

Received 30 March 2006; published 6 September 2006

Realcollective density variables C(k) [cf. Eq. (1.3)] in many-particle systemsarise from nonlinear transformations of particle positions, and determine thestructure factor S(k), where k denotes the wave vector. Ourobjective is to prescribe C(k) and then to find many-particleconfigurations that correspond to such a target C(k) using anumerical optimization technique. Numerical results reported here extend earlier one-and two-dimensional studies to include three dimensions. In addition, theydemonstrate the capacity to control S(k) in the neighborhood of|k|=0. The optimization method employed generates multiparticle configurations for whichS(k) [proportional] |k|, |k|K, and alpha =1, 2, 4, 6, 8, and 10.The case alpha =1 is relevant for the Harrison-Zeldovich model ofthe early universe, for superfluid ⁴He, and for jammed amorphoussphere packings. The analysis also provides specific examples of interactionpotentials whose classical ground states are configurationally degenerate and disordered.

URL:	http://link.aps.org/doi/10.1103/PhysRevE.74.031104
DOI:	10.1103/PhysRevE.74.031104
PACS:	05.70.Fh; 05.20.Jj 05.70.Fh Phase transitions: general studies 05.20.Jj Statistical mechanics of classical fluids YEAR: 2006
KEYWORDS:	phase transformations, statistical mechanics

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