Y.Y. Li, K.S. Leung, et al.
J Combin Optim
The use of spline functions to approximate the "effective" interparticle potentials that result from taking into account all image particles in periodic-boundary-condition Monte Carlo or molecular dynamics simulations is described. Such approximations are intrinsically very "smooth," easy to construct, relatively inexpensive to evaluate and can provide a high degree of accuracy. The asymptotic properties of systems governed by long-range interactions may thus be determined using relatively small particle numbers. A number of implementation issues are discussed in detail, including the choice of end conditions, economical storage of the spline coefficients, conversion to B-spline form, and efficient evaluation procedures. Applied to the problem of locating the melting temperature Tm of a Yukawa system by means of molecular dynamics simulations, we observe values for Tm that are virtually independent of the particle number N if the pair potential includes the spline correction term and N ≥ 250, whereas using only the "minimum image" method gives Tm values that systematically decrease and attain the asymptotic value only for N ≥ 5000. © 1994 Academic Press. All rights reserved.
Y.Y. Li, K.S. Leung, et al.
J Combin Optim
Harpreet S. Sawhney
IS&T/SPIE Electronic Imaging 1994
Ronen Feldman, Martin Charles Golumbic
Ann. Math. Artif. Intell.
M. Shub, B. Weiss
Ergodic Theory and Dynamical Systems