Accurate calculation of functions used in a model of the nematic behavior of self-assembling systems
HTML articles powered by AMS MathViewer
- by Alan E. Berger PDF
- Math. Comp. 54 (1990), 313-330 Request permission
Abstract:
An algorithm used to evaluate double sums arising in a model describing the nematic phase behavior of surfactant solutions is demonstrated to yield approximations accurate to within a tenth of a percent. When direct summation would converge slowly, an asymptotic result is employed based on a double application of the Euler-Maclaurin sum formula.References
-
M. Abramowitz and I. A. Stegun, Handbook of mathematical functions, Dover, New York, ninth printing.
I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, Academic Press, New York, 1980.
J. Herzfeld, Liquid crystalline order in self-assembling systems: orientation dependence of the particle size distribution, J. Chem. Phys. 88 (1988), 2776-2779.
- F. B. Hildebrand, Introduction to numerical analysis, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1956. MR 0075670 M. P. Taylor, A. E. Berger and J. Herzfeld, Theory of liquid crystalline phases in amphiphilic systems, Molecular Crystals and Liquid Crystals 157 (1988), 489-500. M. P. Taylor, A. E. Berger and J. Herzfeld, Theory of amphiphilic liquid crystals: multiple phase transitions in a model micellar system, J. Chem. Phys. 91 (1989), 528-538.
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Math. Comp. 54 (1990), 313-330
- MSC: Primary 65D20; Secondary 65B10, 82A57
- DOI: https://doi.org/10.1090/S0025-5718-1990-0990597-7
- MathSciNet review: 990597