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Discrete models of force chain networks
Positive feedback control of Rayleigh-Bénard convection
1. | Weierstrass-Institute for Applied Analysis and Stochastics, Mohrenstr. 39 D-10117 Berlin, Germany |
2. | Department of Mathematics, Duke University, Durham, NC 27708, Department of Mathematics, Univ. of California Los Angeles, Los Angeles, CA 90095, United States |
3. | Department of Mechanical Engineering, Center for Nonlinear and Complex Systems, Duke University, Durham, NC 27708, United States |
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Tian Ma, Shouhong Wang. Attractor bifurcation theory and its applications to Rayleigh-Bénard convection. Communications on Pure and Applied Analysis, 2003, 2 (4) : 591-599. doi: 10.3934/cpaa.2003.2.591 |
[2] |
Tingyuan Deng. Three-dimensional sphere $S^3$-attractors in Rayleigh-Bénard convection. Discrete and Continuous Dynamical Systems - B, 2010, 13 (3) : 577-591. doi: 10.3934/dcdsb.2010.13.577 |
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Toshiyuki Ogawa. Bifurcation analysis to Rayleigh-Bénard convection in finite box with up-down symmetry. Communications on Pure and Applied Analysis, 2006, 5 (2) : 383-393. doi: 10.3934/cpaa.2006.5.383 |
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Jungho Park. Dynamic bifurcation theory of Rayleigh-Bénard convection with infinite Prandtl number. Discrete and Continuous Dynamical Systems - B, 2006, 6 (3) : 591-604. doi: 10.3934/dcdsb.2006.6.591 |
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Jhean E. Pérez-López, Diego A. Rueda-Gómez, Élder J. Villamizar-Roa. On the Rayleigh-Bénard-Marangoni problem: Theoretical and numerical analysis. Journal of Computational Dynamics, 2020, 7 (1) : 159-181. doi: 10.3934/jcd.2020006 |
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Björn Birnir, Nils Svanstedt. Existence theory and strong attractors for the Rayleigh-Bénard problem with a large aspect ratio. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 53-74. doi: 10.3934/dcds.2004.10.53 |
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Marco Cabral, Ricardo Rosa, Roger Temam. Existence and dimension of the attractor for the Bénard problem on channel-like domains. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 89-116. doi: 10.3934/dcds.2004.10.89 |
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O. V. Kapustyan, V. S. Melnik, José Valero. A weak attractor and properties of solutions for the three-dimensional Bénard problem. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 449-481. doi: 10.3934/dcds.2007.18.449 |
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Petr Knobloch. Error estimates for a nonlinear local projection stabilization of transient convection--diffusion--reaction equations. Discrete and Continuous Dynamical Systems - S, 2015, 8 (5) : 901-911. doi: 10.3934/dcdss.2015.8.901 |
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Roland Pulch. Stability preservation in Galerkin-type projection-based model order reduction. Numerical Algebra, Control and Optimization, 2019, 9 (1) : 23-44. doi: 10.3934/naco.2019003 |
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ShinJa Jeong, Mi-Young Kim. Computational aspects of the multiscale discontinuous Galerkin method for convection-diffusion-reaction problems. Electronic Research Archive, 2021, 29 (2) : 1991-2006. doi: 10.3934/era.2020101 |
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Andrzej Just, Zdzislaw Stempień. Optimal control problem for a viscoelastic beam and its galerkin approximation. Discrete and Continuous Dynamical Systems - B, 2018, 23 (1) : 263-274. doi: 10.3934/dcdsb.2018018 |
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Maya Bassam, Denis Mercier, Ali Wehbe. Optimal energy decay rate of Rayleigh beam equation with only one boundary control force. Evolution Equations and Control Theory, 2015, 4 (1) : 21-38. doi: 10.3934/eect.2015.4.21 |
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Zhen-Zhen Tao, Bing Sun. Galerkin spectral method for elliptic optimal control problem with $L^2$-norm control constraint. Discrete and Continuous Dynamical Systems - B, 2022, 27 (8) : 4121-4141. doi: 10.3934/dcdsb.2021220 |
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Gildas Besançon, Didier Georges, Zohra Benayache. Towards nonlinear delay-based control for convection-like distributed systems: The example of water flow control in open channel systems. Networks and Heterogeneous Media, 2009, 4 (2) : 211-221. doi: 10.3934/nhm.2009.4.211 |
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Konstantinos Chrysafinos, Efthimios N. Karatzas. Symmetric error estimates for discontinuous Galerkin approximations for an optimal control problem associated to semilinear parabolic PDE's. Discrete and Continuous Dynamical Systems - B, 2012, 17 (5) : 1473-1506. doi: 10.3934/dcdsb.2012.17.1473 |
[17] |
Mats Gyllenberg, Yan Ping. The generalized Liénard systems. Discrete and Continuous Dynamical Systems, 2002, 8 (4) : 1043-1057. doi: 10.3934/dcds.2002.8.1043 |
[18] |
Hung-Wen Kuo. The initial layer for Rayleigh problem. Discrete and Continuous Dynamical Systems - B, 2011, 15 (1) : 137-170. doi: 10.3934/dcdsb.2011.15.137 |
[19] |
Na Li, Maoan Han, Valery G. Romanovski. Cyclicity of some Liénard Systems. Communications on Pure and Applied Analysis, 2015, 14 (6) : 2127-2150. doi: 10.3934/cpaa.2015.14.2127 |
[20] |
Jaume Llibre, Claudia Valls. On the analytic integrability of the Liénard analytic differential systems. Discrete and Continuous Dynamical Systems - B, 2016, 21 (2) : 557-573. doi: 10.3934/dcdsb.2016.21.557 |
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