Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Exact evaluation of the integral involved in Doi-Edwards constitutive equations

Author: V. I. Fabrikant
Journal: Quart. Appl. Math. 70 (2012), 787-792
MSC (2000): Primary 76A05, 33E05
DOI: https://doi.org/10.1090/S0033-569X-2012-01273-1
Published electronically: July 18, 2012
MathSciNet review: 3052091
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A basic two-dimensional integral, used for establishment of a connection between the stress and the strain tensor, is evaluated exactly and in closed form in terms of elliptic integrals of the first and the second kind. This integral has not been evaluated before. Our result will allow exact analysis of entangled polymeric systems. A generalization of the basic integral is presented in the last section.

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

  • 1. H. Bateman and A. Erdélyi, Higher Transcendental Functions, Vol. 1, McGraw-Hill, 1953. MR 0058756 (15:419i)
  • 2. H. Bateman and A. Erdélyi, Higher Transcendental Functions, Vol. 3, McGraw-Hill, 1955. MR 0066496 (16:586c)
  • 3. M. Doi and S.F. Edwards, The theory of polymer dynamics, Oxford University Press, New York, 1991.
  • 4. I.S. Gradshteyn and I.M. Ryzhik, Tables of Integrals, Series and Products, Moscow, 1963. English translation: Academic Press Inc., Boston, 1994. MR 1243179 (94g:00008)
  • 5. O. Hassager and R. Hansen, Constitutive equations for the Doi-Edwards model without independent alignment. Rheol. Acta, 2010, Vol. 49, pp. 555-562.
  • 6. J.M.R. Marin and H.K. Rasmussen, Lagrangian finite-element method for the simulation of K-BKZ fluids with third order accuracy. J. Non-Newtonian Fluid Mechanics, 2009, Vol. 156, pp. 177-188.

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC (2000): 76A05, 33E05

Retrieve articles in all journals with MSC (2000): 76A05, 33E05

Additional Information

V. I. Fabrikant
Affiliation: prisoner $#$167932D, Archambault Jail, 242 Montée Gagnon, Ste-Anne-des-Plaines, Quebec, Canada J0N 1H0
Email: valery{\textunderscore}fabrikant@hotmail.com

DOI: https://doi.org/10.1090/S0033-569X-2012-01273-1
Received by editor(s): March 8, 2011
Published electronically: July 18, 2012
Article copyright: © Copyright 2012 Brown University
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society