Kinetic models for polymers with inertial effects

Pierre Degond; Hailiang Liu

doi:10.3934/nhm.2009.4.625

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2009, Volume 4, Issue 4: 625-647. Doi: 10.3934/nhm.2009.4.625

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Kinetic models for polymers with inertial effects

Pierre Degond^1, and
Hailiang Liu^2,

1.
3-Université de Toulouse (UPS, INSA, UT1, UTM) & CNRS, Institut de Mathématiques de Toulouse (UMR 5219), 118 Route de Narbonne, F-31062 Toulouse
2.
Department of Mathematics, Iowa State University, Ames, IA 50011

Received: January 2009

Revised: September 2009

Published: December 2009

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Abstract

Novel kinetic models for both Dumbbell-like and rigid-rod like polymers are derived, based on the probability distribution function $f(t, x, n, \dot n)$ for a polymer molecule positioned at $x$ to be oriented along direction $n$ while embedded in a $\dot n$ environment created by inertial effects. It is shown that the probability distribution function of the extended model, when converging, will lead to well accepted kinetic models when inertial effects are ignored such as the Doi models for rod like polymers, and the Finitely Extensible Non-linear Elastic (FENE) models for Dumbbell like polymers.

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Mathematics Subject Classification: Primary: 76A05, 82A51, 82D60; Secondary: 82A40.

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