On the Simulation of Kinetic Theory Models of Complex Fluids Using the Fokker-Planck Approach
Models of kinetic theory provide a coarse-grained description of molecular configurations wherein atomistic processes are ignored. The Fokker-Planck equation related to the kinetic theory descriptions must be solved for the distribution function in both physical and configuration spaces. When the mo...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2007-04-01
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| Series: | Applied Rheology |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/arh-2007-0006 |
| _version_ | 1818362601825894400 |
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| author | Mokdad B. Pruliere E. Ammar A. Chinesta F. |
| author_facet | Mokdad B. Pruliere E. Ammar A. Chinesta F. |
| author_sort | Mokdad B. |
| collection | DOAJ |
| description | Models of kinetic theory provide a coarse-grained description of molecular configurations wherein atomistic processes are ignored. The Fokker-Planck equation related to the kinetic theory descriptions must be solved for the distribution function in both physical and configuration spaces. When the model involves high dimensional spaces (including physical and conformation spaces and time) standard discretization techniques fail due to excessive computation requirements. In this paper, we revisit some model reduction techniques recently proposed to circumvent those difficulties, exploring other new application areas related to entangled polymer models as well as the use of such reduced models for treating complex flows in which the distribution function involves both the physical and the conformation coordinates. |
| first_indexed | 2024-12-13T21:35:11Z |
| format | Article |
| id | doaj.art-5f544e37f1304b7984897d80c24c61eb |
| institution | Directory Open Access Journal |
| issn | 1617-8106 |
| language | English |
| last_indexed | 2024-12-13T21:35:11Z |
| publishDate | 2007-04-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Applied Rheology |
| spelling | doaj.art-5f544e37f1304b7984897d80c24c61eb2022-12-21T23:30:41ZengDe GruyterApplied Rheology1617-81062007-04-0117226494-126494-1410.1515/arh-2007-0006On the Simulation of Kinetic Theory Models of Complex Fluids Using the Fokker-Planck ApproachMokdad B.0Pruliere E.1Ammar A.2Chinesta F.3Laboratoire de Rhéologie UMR 5520 CNRS-INPG-UJF, 1301 rue de la piscine, BP 53 Domaine Universitaire, 38041Grenoble Cedex 9, FranceLaboratoire de Rhéologie UMR 5520 CNRS-INPG-UJF, 1301 rue de la piscine, BP 53 Domaine Universitaire, 38041Grenoble Cedex 9, FranceLaboratoire de Rhéologie UMR 5520 CNRS-INPG-UJF, 1301 rue de la piscine, BP 53 Domaine Universitaire, 38041Grenoble Cedex 9, FranceLaboratoire de Mécanique des Systèmes et des Procédés, UMR 8106 CNRS-ENSAM-ESEM, 151 Boulevard de l’Hôpital, 75013Paris, FranceModels of kinetic theory provide a coarse-grained description of molecular configurations wherein atomistic processes are ignored. The Fokker-Planck equation related to the kinetic theory descriptions must be solved for the distribution function in both physical and configuration spaces. When the model involves high dimensional spaces (including physical and conformation spaces and time) standard discretization techniques fail due to excessive computation requirements. In this paper, we revisit some model reduction techniques recently proposed to circumvent those difficulties, exploring other new application areas related to entangled polymer models as well as the use of such reduced models for treating complex flows in which the distribution function involves both the physical and the conformation coordinates.https://doi.org/10.1515/arh-2007-0006kinetic theoryfokker-planck equationmodel reductionseparated representationkarhunen-loève decomposition |
| spellingShingle | Mokdad B. Pruliere E. Ammar A. Chinesta F. On the Simulation of Kinetic Theory Models of Complex Fluids Using the Fokker-Planck Approach Applied Rheology kinetic theory fokker-planck equation model reduction separated representation karhunen-loève decomposition |
| title | On the Simulation of Kinetic Theory Models of Complex Fluids Using the Fokker-Planck Approach |
| title_full | On the Simulation of Kinetic Theory Models of Complex Fluids Using the Fokker-Planck Approach |
| title_fullStr | On the Simulation of Kinetic Theory Models of Complex Fluids Using the Fokker-Planck Approach |
| title_full_unstemmed | On the Simulation of Kinetic Theory Models of Complex Fluids Using the Fokker-Planck Approach |
| title_short | On the Simulation of Kinetic Theory Models of Complex Fluids Using the Fokker-Planck Approach |
| title_sort | on the simulation of kinetic theory models of complex fluids using the fokker planck approach |
| topic | kinetic theory fokker-planck equation model reduction separated representation karhunen-loève decomposition |
| url | https://doi.org/10.1515/arh-2007-0006 |
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