American Institute of Mathematical Sciences

Advanced
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
[1]

Ionel Sorin Ciuperca, Erwan Hingant, Liviu Iulian Palade, Laurent Pujo-Menjouet. Fragmentation and monomer lengthening of rod-like polymers, a relevant model for prion proliferation. Discrete & Continuous Dynamical Systems - B, 2012, 17 (3) : 775-799. doi: 10.3934/dcdsb.2012.17.775
[2]

Young-Pil Choi, Seok-Bae Yun. A BGK kinetic model with local velocity alignment forces. Networks & Heterogeneous Media, 2020, 15 (3) : 389-404. doi: 10.3934/nhm.2020024
[3]

Giuseppe Toscani. A kinetic description of mutation processes in bacteria. Kinetic & Related Models, 2013, 6 (4) : 1043-1055. doi: 10.3934/krm.2013.6.1043
[4]

John W. Barrett, Endre Süli. Existence of global weak solutions to Fokker-Planck and Navier-Stokes-Fokker-Planck equations in kinetic models of dilute polymers. Discrete & Continuous Dynamical Systems - S, 2010, 3 (3) : 371-408. doi: 10.3934/dcdss.2010.3.371
[5]

Paolo Barbante, Aldo Frezzotti, Livio Gibelli. A kinetic theory description of liquid menisci at the microscale. Kinetic & Related Models, 2015, 8 (2) : 235-254. doi: 10.3934/krm.2015.8.235
[6]

Adriano Festa, Andrea Tosin, Marie-Therese Wolfram. Kinetic description of collision avoidance in pedestrian crowds by sidestepping. Kinetic & Related Models, 2018, 11 (3) : 491-520. doi: 10.3934/krm.2018022
[7]

Ondřej Kreml, Milan Pokorný. On the local strong solutions for the FENE dumbbell model. Discrete & Continuous Dynamical Systems - S, 2010, 3 (2) : 311-324. doi: 10.3934/dcdss.2010.3.311
[8]

Wendi Wang. Epidemic models with nonlinear infection forces. Mathematical Biosciences & Engineering, 2006, 3 (1) : 267-279. doi: 10.3934/mbe.2006.3.267
[9]

Xiao-Dong Yang, Roderick V. N. Melnik. Accounting for the effect of internal viscosity in dumbbell models for polymeric fluids and relaxation of DNA. Conference Publications, 2007, 2007 (Special) : 1052-1060. doi: 10.3934/proc.2007.2007.1052
[10]

Sebastián Ferrer, Francisco Crespo. Parametric quartic Hamiltonian model. A unified treatment of classic integrable systems. Journal of Geometric Mechanics, 2014, 6 (4) : 479-502. doi: 10.3934/jgm.2014.6.479
[11]

Ghendrih Philippe, Hauray Maxime, Anne Nouri. Derivation of a gyrokinetic model. Existence and uniqueness of specific stationary solution. Kinetic & Related Models, 2009, 2 (4) : 707-725. doi: 10.3934/krm.2009.2.707
[12]

Elena Rossi. A justification of a LWR model based on a follow the leader description. Discrete & Continuous Dynamical Systems - S, 2014, 7 (3) : 579-591. doi: 10.3934/dcdss.2014.7.579
[13]

Angélique Perrillat-Mercerot, Alain Miranville, Nicolas Bourmeyster, Carole Guillevin, Mathieu Naudin, Rémy Guillevin. What mathematical models can or cannot do in glioma description and understanding. Discrete & Continuous Dynamical Systems - S, 2020, 13 (8) : 2165-2193. doi: 10.3934/dcdss.2020184
[14]

Elvise Berchio, Filippo Gazzola. The role of aerodynamic forces in a mathematical model for suspension bridges. Conference Publications, 2015, 2015 (special) : 112-121. doi: 10.3934/proc.2015.0112
[15]

Dieter Armbruster, Matthew Wienke. Kinetic models and intrinsic timescales: Simulation comparison for a 2nd order queueing model. Kinetic & Related Models, 2019, 12 (1) : 177-193. doi: 10.3934/krm.2019008
[16]

Faker Ben Belgacem. Uniqueness for an ill-posed reaction-dispersion model. Application to organic pollution in stream-waters. Inverse Problems & Imaging, 2012, 6 (2) : 163-181. doi: 10.3934/ipi.2012.6.163
[17]

Seung-Yeal Ha, Doron Levy. Particle, kinetic and fluid models for phototaxis. Discrete & Continuous Dynamical Systems - B, 2009, 12 (1) : 77-108. doi: 10.3934/dcdsb.2009.12.77
[18]

Michael Herty, Gabriella Puppo, Sebastiano Roncoroni, Giuseppe Visconti. The BGK approximation of kinetic models for traffic. Kinetic & Related Models, 2020, 13 (2) : 279-307. doi: 10.3934/krm.2020010
[19]

Lingbing He, Claude Le Bris, Tony Lelièvre. Periodic long-time behaviour for an approximate model of nematic polymers. Kinetic & Related Models, 2012, 5 (2) : 357-382. doi: 10.3934/krm.2012.5.357
[20]

Shuichi Kawashima, Peicheng Zhu. Traveling waves for models of phase transitions of solids driven by configurational forces. Discrete & Continuous Dynamical Systems - B, 2011, 15 (1) : 309-323. doi: 10.3934/dcdsb.2011.15.309

2019 Impact Factor: 1.053

Tools

Metrics

  • PDF downloads (38)
  • HTML views (0)
  • Cited by (21)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences