Obioma U. Uche,¹ Salvatore Torquato,^2,3,4,5 and Frank H. Stillinger²

¹ Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544, USA
² Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
³ Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA
⁴ Program in Applied & Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
⁵ Princeton Center for Theoretical Physics, Princeton University, Princeton, New Jersey 08544, USA

(Received 30 March 2006; published 6 September 2006)

Phys. Rev. E 74, 031104 (2006)

Abstract

Real collective density variables C(k) [cf. Eq. (1.3)] in many-particle systems arise from nonlinear transformations of particle positions, and determine the structure factor S(k), where k denotes the wave vector. Our objective is to prescribe C(k) and then to find many-particle configurations that correspond to such a target C(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(k) in the neighborhood of |k|=0. The optimization method employed generates multiparticle configurations for which S(k)µ|k|^a, |k|£K, and a=1, 2, 4, 6, 8, and 10. The case a=1 is relevant for the Harrison-Zeldovich model of the early universe, for superfluid ⁴He, and for jammed amorphous sphere packings. The analysis also provides specific examples of interaction potentials whose classical ground states are configurationally degenerate and disordered.