American Institute of Mathematical Sciences

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December  2009, 4(4): 625-647. doi: 10.3934/nhm.2009.4.625

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  October 2009

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.
Keywords: kinetic description, Dumbbell model., Brownian forces, Polymers, Rod like models.
Mathematics Subject Classification: Primary: 76A05, 82A51, 82D60; Secondary: 82A4.
Citation: Pierre Degond, Hailiang Liu. Kinetic models for polymers with inertial effects. Networks & Heterogeneous Media, 2009, 4 (4) : 625-647. doi: 10.3934/nhm.2009.4.625
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