Linear and nonlinear front instabilities in bistable systems

Physica D: Nonlinear Phenomena

Volumn 217, Issue 2, 2006, Pages 186-192

  Hagberg, A ^a   Yochelis, A ^b   Yizhaq, H ^c   Elphick, C ^d   Pismen, L ^e   Meron, E ^c  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

^d Centro de Fisica No Lineal y Sistemas Complejos de Santiago   (Chile)

^e TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Front instabilities; Nonlinear dynamics; Pattern formation; Swift Hohenberg equation

Indexed keywords

DYNAMICS; NONLINEAR OPTICS; PATTERN RECOGNITION; PERTURBATION TECHNIQUES;

FRONT INSTABILITIES; LABYRINTHINE PATTERNS; PATTERN FORMATION; SWIFT-HOHENBERG EQUATION;

OPTICAL BISTABILITY;

EID: 33744799485     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2006.04.005     Document Type: Article

References (28)

1. Lee K.J., and Swinney H.L. Lamellar structures and self-replicating spots in a reaction-diffusion system. Phys. Rev. E 51 (1995) 1899
2. Yochelis A., Hagberg A., Meron E., Lin A.L., and Swinney H.L. Development of standing-wave labyrinthine patterns. SIADS 1 2 (2002) 236-247
3. Nasuno S., Yoshimo N., and Kai S. Structural transition and motion of domain walls in liquid crystals under a rotating magnetic field. Phys. Rev. E 51 (1995) 1598
4. Frisch T., and Gilli J.M. Excitability and defect-mediated turbulence in nematic liquid crystal. J. Phys. II France 5 (1995) 561-572
5. Marts B., Hagberg A., Meron E., and Lin A.L. Bloch-front turbulence in a periodically forced Belousov-Zhabotinsky reaction. Phys. Rev. Lett. 93 (2004) 108305
6. Coullet P., and Emilsson K. Strong resonances of spatially distributed oscillators: A laboratory to study patterns and defects. Physica D 61 (1992) 119-131
7. Bode M., Reuter A., Schmeling R., and Purwins H.-G. Measurement of the transition from uni-to-bi-directional front propagation in a reaction-diffusion system. Phys. Lett. A 185 (1994) 70
8. Hagberg A., and Meron E. From labyrinthine patterns to spiral turbulence. Phys. Rev. Lett. 72 15 (1994) 2494-2497
9. Hagberg A., and Meron E. Complex patterns in reaction-diffusion systems: A tale of two front instabilities. Chaos 4 3 (1994) 477-484
10. Aranson I.S., Malomed B.A., Pismen L.M., and Tsimring L.S. Crystallization kinetics and self-induced pinning in cellular patterns. Phys. Rev. E 62 (2000) R5-R8
11. Coullet P., Riera C., and Tresser C. Stable static localized structures in one dimension. Phys. Rev. Lett. 84 (2000) 3069-3072
12. Dewel G., Métens S., Hilali MF., Borckmans P., and Price C.B. Resonant patterns through coupling with a zero mode. Phys. Rev. Lett. 74 (1995) 4647-4650
13. Hilali M., Dewel G., and Borckmans P. Subharmonic and strong resonances through coupling with a zero mode. Phys. Lett. A 217 (1996) 263-268
14. Métens S., Dewel G., Borckmans P., and Engelhardt R. Pattern selection in bistable reaction-diffusion systems. Europhys. Lett. 37 (1997) 109
15. Yochelis A., Elphick C., Hagberg A., and Meron E. Frequency locking in extended systems: The impact of a Turing mode. Europhys. Lett. 69 (2005) 170-176
16. Firth W.J., Scroggie A.J., and McDonald G.S. Hexagonal patterns in optical bistability. Phys. Rev. A 46 (1992) R3609-R3612
17. Ahlers G., Berge L.I., and Cannell D.S. Thermal convection in the presence of a first-order phase change. Phys. Rev. Lett 70 (1993) 2399-2402
18. Ackemann T., Logvin Y.A., Heuer A., and Lange W. Transition between positive and negative hexagons in optical pattern formation. Phys. Rev. Lett. 75 (1995) 3450-3453
19. Breazeal W., Flynn K.M., and Gwinn E.G. Static and dynamic two-dimensional patterns in self-extinguishing discharge avalanches. Phys. Rev. E 52 (1995) 1503-1515
20. Yizhaq H., Portnov B.A., and Meron E. A mathematical model of segregation patterns in residential neighbourhoods. Environ. Planning A 36 (2004) 149-173
21. Passot T., and Newell A.C. Towards a universal theory for natural patterns. Physica D 74 (1994) 301-352
22. Supplemental material can be found athttp://math.lanl.gov/nonlinearfront/
23. H. Yizhaq, Population dynamics: Urban segregation as a nonlinear phenomenon, Ph.D. Thesis, Ben Gurion University, 2003
24. T as resulting from fingering and tip-splitting processes that follow a linear transverse front instability [8]
25. Ouchi K., and Fujisaka H. Phase ordering kinetics in the Swift-Hohenberg equation. Phys. Rev. E 54 (1996) 3895-3898
26. Newell A.C., Passot T., Ercolani N., and Indik R. Elementary and composite defects of striped patterns. J. Phys. II France 5 (1995) 1863-1882
27. Umbanhowar P.B., Melo F., and Swinney H.L. Periodic, aperiodic, and transient patterns in vibrated granular layers. Physica A 249 (1998) 1-9
28. Aranson I.S., Blair D., Kwok W.K., Karapetrov G., Welp U., Crabtree G.W., Vinokur V.M., and Tsimring L.S. Controlled dynamics of interfaces in a vibrated granular layer. Phys. Rev. Lett. 82 4 (1999) 731-734