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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


Accurate calculation of functions used in a model of the nematic behavior of self-assembling systems

Author: Alan E. Berger
Journal: Math. Comp. 54 (1990), 313-330
MSC: Primary 65D20; Secondary 65B10, 82A57
MathSciNet review: 990597
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] M. Abramowitz and I. A. Stegun, Handbook of mathematical functions, Dover, New York, ninth printing.
  • [2] I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, Academic Press, New York, 1980.
  • [3] J. Herzfeld, Liquid crystalline order in self-assembling systems: orientation dependence of the particle size distribution, J. Chem. Phys. 88 (1988), 2776-2779.
  • [4] F. B. Hildebrand, Introduction to numerical analysis, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1956. MR 0075670 (17,788d)
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  • [6] 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.

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Additional Information

PII: S 0025-5718(1990)0990597-7
Keywords: Asymptotics, double sums, Euler-Maclaurin formula, exponential integral function, nematic, phase behavior, surfactant, self-assembling
Article copyright: © Copyright 1990 American Mathematical Society

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