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Existence of solution for a system of repulsion and alignment: Comparison between theory and simulation
1. | 1-Université de Toulouse; UPS, INSA, UT1, UTM, 2-CNRS, Institut de Mathématiques de Toulouse, F-31062 Toulouse, France |
References:
[1] |
A. Barbaro and P. Degond, Phase transition and diffusion among socially interacting self-propelled agents, Discrete Contin. Dyn. Syst. Ser. B, 19 (2014), 1249-1278.
doi: 10.3934/dcdsb.2014.19.1249. |
[2] |
A. Baskaran and M. C. Marchetti, Hydrodynamics of self-propelled hard rods, Phys. Rev. E, 77 (2008), 011920, 9PP.
doi: 10.1103/PhysRevE.77.011920. |
[3] |
E. Bertin, M. Droz and G. Grégoire, Hydrodynamic equations for self-propelled particles: Microscopic derivation and stability analysis, J. Phys. A: Math. Theor., 42 (2009), 445001.
doi: 10.1088/1751-8113/42/44/445001. |
[4] |
A. Cziròk and T. Vicsek, Collective behavior of interacting self-propelled particles, Physica A, 281 (2000), 17-29.
doi: 10.1016/S0378-4371(00)00013-3. |
[5] |
P. Degond, G. Dimarco , T. B. N. Mac and N. Wang, Macroscopic models of collective motion with repulsion, Communications in Mathematical Sciences, 13 (2015), 1615-1638.
doi: 10.4310/CMS.2015.v13.n6.a12. |
[6] |
P. Degond, A. Frouvelle and J.-G. Liu, Macroscopic limits and phase transition in a system of self-propelled particles, J. Nonlinear Sci., 23 (2013), 427-456.
doi: 10.1007/s00332-012-9157-y. |
[7] |
P. Degond, A. Frouvelle, J.-G. Liu, S. Motsch and L. Navoret, Macroscopic models of collective motion and self-organization,, Séminaire Laurent Schwartz — EDP et applications, (): 2012.
doi: 10.5802/slsedp.32. |
[8] |
P. Degond, A. Frouvelle and J.-G. Liu, Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics, Archive for Rational Mechanics and Analysis, 216 (2015), 63-115.
doi: 10.1007/s00205-014-0800-7. |
[9] |
P. Degond and S. Motsch, Continuum limit of self-driven particles with orientation interaction, Math. Models Methods Appl. Sci., 18 (2008), 1193-1215.
doi: 10.1142/S0218202508003005. |
[10] |
P. Degond, J.-G. Liu, S. Motsch and V. Panferov, Hydrodynamic models of self-organized dynamics: Derivation and existence theory, Methods Appl. Anal., 20 (2013), 89-114.
doi: 10.4310/MAA.2013.v20.n2.a1. |
[11] |
A. Frouvelle, A continuum model for alignment of self-propelled particles with anisotropy and density-dependent parameters, Math. Mod. Meth. Appl. Sci., 22 (2012), 1250011, 40pp.
doi: 10.1142/S021820251250011X. |
[12] |
A. Frouvelle and J.-G. Liu, Dynamics in a kinetic model of oriented particles with phase transition, SIAM J. Math. Anal., 44 (2012), 791-826.
doi: 10.1137/110823912. |
[13] |
S. Henkes, Y. Fily and M. C. Marchetti, Active jamming: Self-propelled soft particles at high density, Phys. Rev. E, 84 (2011), 040301.
doi: 10.1103/PhysRevE.84.040301. |
[14] |
S. Motsch and L. Navoret, Numerical simulations of a non-conservative hyperbolic system with geometric constraints describing swarming behavior, Multiscale Model. Simul., 9 (2011), 1253-1275.
doi: 10.1137/100794067. |
[15] |
F. Peruani, A. Deutsch and M. Bär, Nonequilibrium clustering of self-propelled rods, Phys. Rev. E, 74 (2006), 030904(R).
doi: 10.1103/PhysRevE.74.030904. |
[16] |
V. I. Ratushnaya, D. Bedeaux, V. L. Kulinskii and A. V. Zvelindovsky, Collective behavior of self propelling particles with kinematic constraints: the relations between the discrete and the continuous description, Phys. A, 381 (2007), 39-46.
doi: 10.1016/j.physa.2007.03.045. |
[17] |
M. E. Taylor, Partial Differential Equations III, Second edition. Applied Mathematical Sciences, 117. Springer, New York, 2011.
doi: 10.1007/978-1-4419-7049-7. |
[18] |
Y. Tu, J. Toner and M. Ulm, Sound waves and the absence of Galilean invariance in flocks, Phys. Rev. Lett., 80 (1998), 4819-4822.
doi: 10.1103/PhysRevLett.80.4819. |
[19] |
T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen and O. Shochet, Novel type of phase transition in a system of self-driven particles, Phys. Rev. Lett., 75 (1995), 1226-1229.
doi: 10.1103/PhysRevLett.75.1226. |
show all references
References:
[1] |
A. Barbaro and P. Degond, Phase transition and diffusion among socially interacting self-propelled agents, Discrete Contin. Dyn. Syst. Ser. B, 19 (2014), 1249-1278.
doi: 10.3934/dcdsb.2014.19.1249. |
[2] |
A. Baskaran and M. C. Marchetti, Hydrodynamics of self-propelled hard rods, Phys. Rev. E, 77 (2008), 011920, 9PP.
doi: 10.1103/PhysRevE.77.011920. |
[3] |
E. Bertin, M. Droz and G. Grégoire, Hydrodynamic equations for self-propelled particles: Microscopic derivation and stability analysis, J. Phys. A: Math. Theor., 42 (2009), 445001.
doi: 10.1088/1751-8113/42/44/445001. |
[4] |
A. Cziròk and T. Vicsek, Collective behavior of interacting self-propelled particles, Physica A, 281 (2000), 17-29.
doi: 10.1016/S0378-4371(00)00013-3. |
[5] |
P. Degond, G. Dimarco , T. B. N. Mac and N. Wang, Macroscopic models of collective motion with repulsion, Communications in Mathematical Sciences, 13 (2015), 1615-1638.
doi: 10.4310/CMS.2015.v13.n6.a12. |
[6] |
P. Degond, A. Frouvelle and J.-G. Liu, Macroscopic limits and phase transition in a system of self-propelled particles, J. Nonlinear Sci., 23 (2013), 427-456.
doi: 10.1007/s00332-012-9157-y. |
[7] |
P. Degond, A. Frouvelle, J.-G. Liu, S. Motsch and L. Navoret, Macroscopic models of collective motion and self-organization,, Séminaire Laurent Schwartz — EDP et applications, (): 2012.
doi: 10.5802/slsedp.32. |
[8] |
P. Degond, A. Frouvelle and J.-G. Liu, Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics, Archive for Rational Mechanics and Analysis, 216 (2015), 63-115.
doi: 10.1007/s00205-014-0800-7. |
[9] |
P. Degond and S. Motsch, Continuum limit of self-driven particles with orientation interaction, Math. Models Methods Appl. Sci., 18 (2008), 1193-1215.
doi: 10.1142/S0218202508003005. |
[10] |
P. Degond, J.-G. Liu, S. Motsch and V. Panferov, Hydrodynamic models of self-organized dynamics: Derivation and existence theory, Methods Appl. Anal., 20 (2013), 89-114.
doi: 10.4310/MAA.2013.v20.n2.a1. |
[11] |
A. Frouvelle, A continuum model for alignment of self-propelled particles with anisotropy and density-dependent parameters, Math. Mod. Meth. Appl. Sci., 22 (2012), 1250011, 40pp.
doi: 10.1142/S021820251250011X. |
[12] |
A. Frouvelle and J.-G. Liu, Dynamics in a kinetic model of oriented particles with phase transition, SIAM J. Math. Anal., 44 (2012), 791-826.
doi: 10.1137/110823912. |
[13] |
S. Henkes, Y. Fily and M. C. Marchetti, Active jamming: Self-propelled soft particles at high density, Phys. Rev. E, 84 (2011), 040301.
doi: 10.1103/PhysRevE.84.040301. |
[14] |
S. Motsch and L. Navoret, Numerical simulations of a non-conservative hyperbolic system with geometric constraints describing swarming behavior, Multiscale Model. Simul., 9 (2011), 1253-1275.
doi: 10.1137/100794067. |
[15] |
F. Peruani, A. Deutsch and M. Bär, Nonequilibrium clustering of self-propelled rods, Phys. Rev. E, 74 (2006), 030904(R).
doi: 10.1103/PhysRevE.74.030904. |
[16] |
V. I. Ratushnaya, D. Bedeaux, V. L. Kulinskii and A. V. Zvelindovsky, Collective behavior of self propelling particles with kinematic constraints: the relations between the discrete and the continuous description, Phys. A, 381 (2007), 39-46.
doi: 10.1016/j.physa.2007.03.045. |
[17] |
M. E. Taylor, Partial Differential Equations III, Second edition. Applied Mathematical Sciences, 117. Springer, New York, 2011.
doi: 10.1007/978-1-4419-7049-7. |
[18] |
Y. Tu, J. Toner and M. Ulm, Sound waves and the absence of Galilean invariance in flocks, Phys. Rev. Lett., 80 (1998), 4819-4822.
doi: 10.1103/PhysRevLett.80.4819. |
[19] |
T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen and O. Shochet, Novel type of phase transition in a system of self-driven particles, Phys. Rev. Lett., 75 (1995), 1226-1229.
doi: 10.1103/PhysRevLett.75.1226. |
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