A New Proof on Axisymmetric Equilibria of a Three-Dimensional Smoluchowski Equation

Abstract

We consider equilibrium solutions of the Smoluchowski equation for rodlike nematic polymers with a Maier-Saupe excluded volume potential. The purpose of this paper is to present a new and simplified proof of classical well-known results: (1) all equilibria are axisymmetric and (2) modulo rotational symmetry, the number and type of axisymmetric equilibria are characterized with respect to the strength of the excluded volume potential. These results confirm the phase diagram of equilibria obtained previously by numerical simulations (Faraoni et al 1999 J. Rheol. 43 829-43, Forest et al 2004 Rheol. Acta 43 17-37, Larson and Ottinger 1991 Macromolecules 24 6270-82).

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Document Details

Document Type
Technical Report
Publication Date
Oct 07, 2005
Accession Number
ADA496432

Entities

People

  • Hong Zhou
  • Hongyun Wang
  • M. G. Forest
  • Qi Wang

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Advanced Materials
  • Applied Mathematics
  • Axisymmetric
  • Calculus
  • Cartesian Coordinates
  • Coordinate Systems
  • Differential Equations
  • Eigenvalues
  • Equations
  • Integral Equations
  • Mathematics
  • Phase Transformations
  • Probability
  • Probability Density Functions
  • Random Variables
  • Symmetry
  • Three Dimensional

Readers

  • Fluid Dynamics.
  • Mathematical Modeling and Probability Theory.
  • Polymer Science and Technology