A bistable reaction-diffusion system in a stretching flow

Physica D: Nonlinear Phenomena

Volumn 216, Issue 2, 2006, Pages 307-318

  Cox, Stephen M ^a   Gottwald, Georg A ^b  

^a UNIVERSITY OF ADELAIDE   (Australia)

^b UNIVERSITY OF SYDNEY   (Australia)

Author keywords

Bistable chemical reaction; Chaotic stirring; Reaction diffusion system

Indexed keywords

DIFFUSION; INITIAL VALUE PROBLEMS; ORDINARY DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES;

BISTABLE CHEMICAL REACTION; CHAOTIC STIRRING; REACTION-DIFFUSION SYSTEM;

FLOW OF FLUIDS;

EID: 33646153550     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2006.03.007     Document Type: Article

References (28)

1. Epstein I.R. The consequences of imperfect mixing in autocatalytic chemical and biological systems. Nature 374 (1995) 321-327
2. Allen M.A., Brindley J., Merkin J., and Piling M.J. Autocatalysis in a shear flow. Phys. Rev. E 54 (1996) 2140-2142
3. Abraham E.R. The generation of plankton patchiness by turbulent stirring. Nature 391 (1998) 577-580
4. Martin A.P. On filament width in oceanic plankton distributions. J. Plank. Res. 22 (2000) 597-692
5. McLeod P., Martin A.P., and Richards K.J. Minimum length scale for growth-limited oceanic plankton distributions. Ecol. Model. 158 (2002) 111-120
6. Hernández-Garcia E., and Lopéz C. Sustained plankton blooms under open chaotic flows. Ecol. Complex. 1 (2004) 193
7. Edouard S., Legras B., Lefèvre F., and Eymard R. The effect of small-scale inhomogeneities on ozone depletion in the Arctic. Nature 384 (1996) 444-447
8. Ronney P.D. Some open issues in premixed turbulent combustion. In: Buckmaster J., and Takeno T. (Eds). Modeling in Combustion Science. Lecture Notes in Physics (1994), Springer-Verlag 3-22
9. Neufeld Z. Excitable media in a chaotic flow. Phys. Rev. Lett. 87 (2001) 108301
10. Neufeld Z., Haynes P.H., and Tél T. Chaotic mixing induced transitions in reaction-diffusion systems. Chaos 12 (2002) 426-438
11. Neufeld Z., Lopéz C., Hernández-Garcia E., and Piro O. Excitable media in open and closed chaotic flows. Phys. Rev. E 66 (2002) 066208
12. Hernández-Garcia E., Lopéz C., and Neufeld Z. Filament bifurcations in a one-dimensional model of reacting excitable fluid flow. Physica A 327 (2003) 59-64
13. Kiss I.Z., Merkin J.H., and Neufeld Z. Combustion initiation and extinction in a 2D chaotic flow. Physica D 183 (2003) 175-189
14. Kiss I.Z., Merkin J.H., Scott S.K., Simon P.L., Kalliadasis S., and Neufeld Z. The structure of flame filaments in chaotic flows. Physica D 176 (2003) 67-81
15. Menon S., and Gottwald G.A. Bifurcations in reaction-diffusion systems in chaotic flows. Phys. Rev. E 71 (2005) 066201
16. Ranz W.E. Applications of a stretched model to mixing, diffusion, and reaction in laminar and turbulent flows. AIChE J. 25 (1979) 41-47
17. Gray P., and Scott S.K. Chemical Oscillations and Instabilities (1994), Clarendon Press, Oxford
18. Ranz W.E. Applications of a stretch model to mixing, diffusion, and reaction in laminar and turbulent flows. AIChE J. 25 (1979) 41-47
19. Tang X.Z., and Boozer A.H. Design criteria of a chemical reactor based on a chaotic flow. Chaos 9 (1999) 183-194
20. Thiffeault J.-L. Advection-diffusion in Lagrangian coordinates. Phys. Lett. A 309 (2003) 415-422
21. Cox S.M. Chaotic mixing of a competitive-consecutive reaction. Physica D 199 (2004) 369-386
22. Murray J.D. Mathematical Biology. 2nd edition (1993), Springer Verlag, New York
23. Keener J., and Sneyd J. Mathematical Physiology (1998), Springer Verlag, New York
24. Mikhailov A.S. Foundations of Synergetics I: Distributed Active Systems. 2nd edition (1994), Springer Verlag, Berlin
25. Scott A. Nonlinear Science - Emergence and Dynamics of Coherent Structures (1999), Oxford University Press, Oxford
26. Gottwald G.A., and Kramer L. On propagation failure in one- and two-dimensional excitable media. Chaos 14 (2004) 855-863
27. Vikhansky A. Quantification of reactive mixing in laminar microflows. Phys. Fluids 16 (2004) 4738-4741
28. Vikhansky A., and Cox S.M. Reduced models of chemical reaction in chaotic flows. Phys. Fluids 18 (2006) 037102