Tailoring the S(k) Behaviour of Point Particle Systems
Collective density variables ρ(k) have proved to be useful tools in the study of many-body problems in a variety of fields that are concerned with structural and kinematic phenomena. In the present investigation, these variables are utilized as the means of tailoring the structure factor S(k) behaviour of point particle systems. Our approach involves constraining related C(k) parameters with wave vector k magnitudes at or below a chosen cutoff, to values that are consistent with the minimization of a quadratic objective function, Φ. We use the MINOP optimization technique in order to achieve sets of particle positions for which Φ = 0. The MINOP algorithm minimizes a real valued function given only first t derivative and function information. In general, it applies a dogleg strategy which uses a gradient direction when one is far from a solution, a quasi-Newton direction when one is close, and a linear combination of the two when at intermediate stages.
Abstract Author(s): O. U. Uche, F. H. Stillinger, D. K. Stillinger, A. Gabrielli, and S. Torquato