Study of the noise-induced transition and the exploration of the phase space for the Kuramoto-Sivashinsky equation using the minimum action method

Nonlinearity

Volumn 23, Issue 3, 2010, Pages 475-493

  Wan, X ^a   Zhou, X ^b   E, W ^b  

^a LOUISIANA STATE UNIVERSITY   (United States)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 75149162388     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/23/3/002     Document Type: Article

References (31)

1. Karmers H A 1940 Brownian motion in a field of force and the diffusion model of chemical reactions Physica 7 284-304
2. Van Kampen N G 1981 Stochastic Processes in Physics and Chemistry (Amsterdam: North-Holland)
3. Wales D J 2003 Energy Landscapes with Application to Clusters, Biomolecules and Glasses (Cambridge: Cambridge University Press)
4. Onsager L and Machlup S 1953 Fluctuations and irreversible processes Phys. Rev. 91 1505-12
5. Ren W 2002 Numerical methods for the study of energy landscape and rare events PhD Thesis New York University
6. E W, Ren W and Vanden-Eijnden E 2002 String method for the study of rare events Phys. Rev. B 66 052301
7. E W, Ren W and Vanden-Eijnden E 2007 Simplified and improved string method for computing the minimum energy paths in barrier-crossing events J. Chem. Phys. 126 164103
8. Jònsson H, Mills G and Jacobsen K W 1998 Nudged elastic band method for finding minimum energy paths of transitions Classical and Quantum Dynamics in Condensed Phase Simulations (LERICI, Villa Marigola) (Proc. of the Int. School of Physics) ed B J Berne et al (Singapore: World Scientific) p 385
9. Cerjan C J and Miller W H 1981 On finding transition states J. Chem. Phys. 75 2800-6
10. Henkelman G and Jónsson H 1999 A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives J. Chem. Phys. 111 7010-22
11. Ren W, E W and Vanden-Eijnden E 2003 Energy landscape and thermally activated switching of submicro-sized ferromagnetic elements J. Appl. Phys. 93 2275
12. Zhou X and E W 2009 Study of noise-induced transitions in the Lorenz system using the minimum action method Commun. Math. Sci. 7 341-55
13. Zhou X 2009 Noise-induce transition pathway in non-gradient systems PhD Thesis Princeton University
14. Kuramoto Y 1978 Diffusion-induced chaos in reactions systems Suppl. Prog. Theor. Phys. 64 346-67
15. Sivashinsky G 1977 Nonlinear analysis of hydrodynamic instability in laminar flames: I. Deviation of basic equations Acta Astron. 4 1177-206 (Pubitemid 8577389)
16. Holmes P, Lumley J L and Berkooz G 1998 Turbulence, Coherent Structures, Dynamical Systems and Symmetry (Cambridge Monographs on Mechanics) (Cambridge: Cambridge University Press)
17. Hyman J M and Nicolaenko B 1986 The Kuramoto-Sivashinsky equation: a bridge between PDE's and dynamical systems Physics D 18 113-26
18. E W, Ren W and Vanden-Eijnden E 2004 Minimum action method for the study of rare events Commun. Pure Appl. Math. 57 637-56
19. Freidlin M I and Wentzell A D 1998 Random perturbations of dynamical systems Grundlehren der Mathematischen Wissenschaften 2 edn (New York: Springer)
20. Zhou X, Ren W and E W 2008 Adaptive minimum action method for the study of rare events J. Chem. Phys. 128 104111
21. Varadhan S R S 1984 Large Deviations and Applications (PA: SIAM)
22. Foias C, Nicolaenko B, Sell G R and Temam R 1988 Inertial manifolds for the Kuramoto-Sivashinsky equation and an estimate of their lowest dimensions J. Math. Pures Appl. 67 197-226
23. Kassam A-K and Trefethen L N 2005 Fourth-order time-stepping for stiff PDEs SIAM J. Sci. Comput. 26 1214-33
24. Hager W W and Zhang H 2005 A new conjugate gradient method with guaranteed descent and an efficient line search SIAM J. Optim. 16 170-92
25. Skufca J D, Yorke J A and Eckhardt B 2006 Edge of chaos in a parallel shear flow Phys. Rev. Lett. 96 174101
26. Schneider T M, Eckhardt B and Yorke J A 2007 Turbulence transition and the edge of chaos in pipe flow Phys. Rev. Lett. 99 034502
27. Maier R S and Stein D L 1993 Escape problem for irreversible systems Phys. Rev. E 48 931-8
28. Gibson J F, Halcrow J and Cvitanovic P 2008 Visualizing the geometry of state space in plane couette flow J. Fluid Mech. 611 107
29. Lan Y 2008 Unstable recurrent patterns in Kuramoto-Sivashinsky dynamics Phys. Rev. E 78 026208
30. Kawahara G and Kida S 2001 Periodic motion embedded in plane couette turbulence: regeneration cycle and burst J. Fluid Mech. 449 291-300
31. Cox S M and Matthews P C 2002 Exponential time differencing for stiff systems J. Comput. Phys. 176 430-55