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On a chemotaxis model with saturated chemotactic flux
A smooth 3D model for fiber lay-down in nonwoven production processes
1. | Fachbereich Mathematik, Technische Universität Kaiserslautern, Germany, Germany |
2. | Fraunhofer ITWM, Kaiserslautern, Germany |
References:
[1] |
W. Albrecht, H. Fuchs and W. Kittelmann, "Nonwoven Fabrics," Wiley, 2003. |
[2] |
L. Arnold, "Stochastic Differential Equations," Springer, 1978. |
[3] |
A. Bensoussan, J.-L. Lions and G. Papanicolaou, "Asymptotic Analysis for Periodic Structures," Studies in Mathematics and its Applications, 5, North-Holland Publishing Co., Amsterdam-New York, 1978. |
[4] |
L. Bonilla and T. Götz, A. Klar, N. Marheineke and R. Wegener, Hydrodynamic limit of a Fokker-Planck equation describing fiber lay-down processes, SIAM J. Appl. Math., 68 (2007/08), 648-665.
doi: 10.1137/070692728. |
[5] |
J.-A. Carrillo, T. Goudon and P. Lafitte, Simulation of fluid and particles flows: Asymptotic preserving schemes for bubbling and flowing regimes, J. Comp. Phys., 227 (2008), 7929-7951.
doi: 10.1016/j.jcp.2008.05.002. |
[6] |
P. Degond and S. Motsch, Large-scale dynamics of the persistent turning walker model of fish behavior, J. Stat. Phys., 131 (2008), 989-1021.
doi: 10.1007/s10955-008-9529-8. |
[7] |
J. Dolbeault, A. Klar, C. Mouhot and C. Schmeiser, Hypocoercivity and a Fokker-Planck equation for fiber lay-down, preprint. |
[8] |
J. Dolbeault, C. Mouhot and C. Schmeiser, Hypocoercivity for kinetic equations with linear relaxation terms, C. R. Acad. Sci. Paris, 347 (2009), 511-516. |
[9] |
T. Götz, A. Klar, N. Marheineke and R. Wegener, A stochastic model and associated Fokker-Planck equation for the fiber lay-down process in nonwoven production processes, SIAM J. Appl. Math., 67 (2007), 1704-1717.
doi: 10.1137/06067715X. |
[10] |
T. Goudon, Hydrodynamic limit for the Vlasov-Poisson-Fokker-Planck system: Analysis of the two-dimensional case, Math. Models Methods Appl. Sci., 15 (2005), 737-752.
doi: 10.1142/S021820250500056X. |
[11] |
J. W. Hearle, M. A. Sultan and S. Govender, The form taken by threads laid on a moving belt, Part I-III, Journal of the Textile Institute, 67 (1976), 373-386.
doi: 10.1080/00405007608630170. |
[12] |
M. Herty, A. Klar, S. Motsch and F. Olawsky, A smooth model for fiber lay-down processes and its diffusion approximations, KRM, 2 (2009), 489-502.
doi: 10.3934/krm.2009.2.489. |
[13] |
A. Klar, N. Marheineke and R. Wegener, Hierarchy of mathematical models for production processes of technical textiles, ZAMM Z. Angew. Math. Mech., 89 (2009), 941-961.
doi: 10.1002/zamm.200900282. |
[14] |
A. Klar, J. Maringer and R. Wegener, A 3D model for fiber lay-down processes in non-woven production processes, to appear in MMMAS. |
[15] |
Y. Kutoyantz, "Statistical Inference for Ergodic Diffusion Processes," Springer, 2004. |
[16] |
L. Mahadevan and J. B. Keller, Coiling of flexible ropes, Proc. R. Soc. Lond. Ser. A, 452 (1996), 1679-1694.
doi: 10.1098/rspa.1996.0089. |
[17] |
N. Marheineke and R. Wegener, Fiber dynamics in turbulent flows: General modeling framework, SIAM J. Appl. Math., 66 (2006), 1703-1726.
doi: 10.1137/050637182. |
[18] |
N. Marheineke and R. Wegener, Modeling and application of a stochastic drag for fibers in turbulent flows, International Journal of Multiphase Flow, 37 (2011), 136-148.
doi: 10.1016/j.ijmultiphaseflow.2010.10.001. |
[19] |
E. Nelson, "Dynamical Theories of Brownian Motion," Princeton University Press, Princeton, N.J., 1967. |
[20] |
M. R. D'Orsogna, V. Panferov and J. A. Carrillo, Double milling in self-propelled swarms from kinetic theory, Kinetic and Related Models, 2 (2009), 363-378.
doi: 10.3934/krm.2009.2.363. |
show all references
References:
[1] |
W. Albrecht, H. Fuchs and W. Kittelmann, "Nonwoven Fabrics," Wiley, 2003. |
[2] |
L. Arnold, "Stochastic Differential Equations," Springer, 1978. |
[3] |
A. Bensoussan, J.-L. Lions and G. Papanicolaou, "Asymptotic Analysis for Periodic Structures," Studies in Mathematics and its Applications, 5, North-Holland Publishing Co., Amsterdam-New York, 1978. |
[4] |
L. Bonilla and T. Götz, A. Klar, N. Marheineke and R. Wegener, Hydrodynamic limit of a Fokker-Planck equation describing fiber lay-down processes, SIAM J. Appl. Math., 68 (2007/08), 648-665.
doi: 10.1137/070692728. |
[5] |
J.-A. Carrillo, T. Goudon and P. Lafitte, Simulation of fluid and particles flows: Asymptotic preserving schemes for bubbling and flowing regimes, J. Comp. Phys., 227 (2008), 7929-7951.
doi: 10.1016/j.jcp.2008.05.002. |
[6] |
P. Degond and S. Motsch, Large-scale dynamics of the persistent turning walker model of fish behavior, J. Stat. Phys., 131 (2008), 989-1021.
doi: 10.1007/s10955-008-9529-8. |
[7] |
J. Dolbeault, A. Klar, C. Mouhot and C. Schmeiser, Hypocoercivity and a Fokker-Planck equation for fiber lay-down, preprint. |
[8] |
J. Dolbeault, C. Mouhot and C. Schmeiser, Hypocoercivity for kinetic equations with linear relaxation terms, C. R. Acad. Sci. Paris, 347 (2009), 511-516. |
[9] |
T. Götz, A. Klar, N. Marheineke and R. Wegener, A stochastic model and associated Fokker-Planck equation for the fiber lay-down process in nonwoven production processes, SIAM J. Appl. Math., 67 (2007), 1704-1717.
doi: 10.1137/06067715X. |
[10] |
T. Goudon, Hydrodynamic limit for the Vlasov-Poisson-Fokker-Planck system: Analysis of the two-dimensional case, Math. Models Methods Appl. Sci., 15 (2005), 737-752.
doi: 10.1142/S021820250500056X. |
[11] |
J. W. Hearle, M. A. Sultan and S. Govender, The form taken by threads laid on a moving belt, Part I-III, Journal of the Textile Institute, 67 (1976), 373-386.
doi: 10.1080/00405007608630170. |
[12] |
M. Herty, A. Klar, S. Motsch and F. Olawsky, A smooth model for fiber lay-down processes and its diffusion approximations, KRM, 2 (2009), 489-502.
doi: 10.3934/krm.2009.2.489. |
[13] |
A. Klar, N. Marheineke and R. Wegener, Hierarchy of mathematical models for production processes of technical textiles, ZAMM Z. Angew. Math. Mech., 89 (2009), 941-961.
doi: 10.1002/zamm.200900282. |
[14] |
A. Klar, J. Maringer and R. Wegener, A 3D model for fiber lay-down processes in non-woven production processes, to appear in MMMAS. |
[15] |
Y. Kutoyantz, "Statistical Inference for Ergodic Diffusion Processes," Springer, 2004. |
[16] |
L. Mahadevan and J. B. Keller, Coiling of flexible ropes, Proc. R. Soc. Lond. Ser. A, 452 (1996), 1679-1694.
doi: 10.1098/rspa.1996.0089. |
[17] |
N. Marheineke and R. Wegener, Fiber dynamics in turbulent flows: General modeling framework, SIAM J. Appl. Math., 66 (2006), 1703-1726.
doi: 10.1137/050637182. |
[18] |
N. Marheineke and R. Wegener, Modeling and application of a stochastic drag for fibers in turbulent flows, International Journal of Multiphase Flow, 37 (2011), 136-148.
doi: 10.1016/j.ijmultiphaseflow.2010.10.001. |
[19] |
E. Nelson, "Dynamical Theories of Brownian Motion," Princeton University Press, Princeton, N.J., 1967. |
[20] |
M. R. D'Orsogna, V. Panferov and J. A. Carrillo, Double milling in self-propelled swarms from kinetic theory, Kinetic and Related Models, 2 (2009), 363-378.
doi: 10.3934/krm.2009.2.363. |
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