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The Equilibrium Theory of Inhomogeneous Polymers$
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Glenn Fredrickson

Print publication date: 2005

Print ISBN-13: 9780198567295

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198567295.001.0001

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The Equilibrium Theory of Inhomogeneous Polymers

Glenn H. Fredrickson

Oxford University Press

This chapter discusses the topic of self-consistent field theory, a mean-field approximation method for analyzing the statistical field models constructed in Chapter 4. The mean-field approximation is introduced as a saddle point approximation to the functional integrals comprising a field theory model. The analytic structure of various models is discussed, along with the classification of saddle points and location in the complex plane. Further analytical approximations to simplify the mean-field equations are described, including weak inhomogeneity and slow gradient expansions, ground state dominance, and strong stretching approximations. Numerical methods for obtaining accurate and efficient solutions of the self-consistent field equations are presented.

Keywords:   field theory, mean-field, self-consistent field, saddle point, random phase approximation, ground state dominance, spectral collocation, pseudo-spectral, unit cell, numerical methods

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