Pattern formation induced by time-dependent advection

Mathematical Modelling of Natural Phenomena

Volumn 6, Issue 1, 2011, Pages 138-148

  Straube, A V ^a,b   Pikovsky, A ^b  

^a HUMBOLDT UNIVERSITY   (Germany)

^b UNIVERSITY OF POTSDAM   (Germany)

Author keywords

pattern formation; reaction advection diffusion equation

Indexed keywords

ARBITRARY TIME; DIFFUSION CONSTANT; HOMOGENEOUS STATE; MIXING FLOW; PATTERN FORMATION; PATTERN-FORMING INSTABILITY; REACTION-ADVECTION-DIFFUSION EQUATION; REACTION-ADVECTION-DIFFUSION SYSTEMS; TIME MODEL; TIME-DEPENDENT ADVECTION; TURING INSTABILITY; TWO COMPONENT SYSTEMS;

DIFFUSION; MATHEMATICAL OPERATORS; PARTIAL DIFFERENTIAL EQUATIONS; STABILITY;

ADVECTION;

EID: 79955528525     PISSN: 09735348     EISSN: 17606101     Source Type: Journal    
DOI: 10.1051/mmnp/20116107     Document Type: Article

References (16)

1. T. M. Antonsen , Z. Fan , E. Ott , E. Garcia-Lopes . The role of chaotic orbits in the determination of power spectra of passive scalars. Phys. Fluids, 8(1996), 3094-3104 (Pubitemid 126616807)
2. L. M. Pismen . Differential flow induced chemical instability and Turing instability for Couette flow. Phys. Rev. E, 58(1998), 4524-4531 (Pubitemid 128596381)
3. J. Huisman , N. N. P. Thi , D. M. Karl , B. Sommeijer . Reduced mixing generates oscillations and chaos in the oceanic deep chlorophyll maximum. Nature, 439(2002), 322-325 (Pubitemid 43128855)
4. Y. Khazan , L. M. Pismen . Differential flow induced chemical instability on a rotating disk. Phys. Rev. Lett., 75 (1995), 4318-4321
5. M. Leconte , J. Martin , N. Rakotomalala , D. Salin . Pattern of reaction diffusion fronts in laminar flows. Phys. Rev. Lett., 90 (2002), 128302
6. G. Nicolis, G. Prigogine. Self-organization in nonequilibrium systems: from dissipative structures to order through fluctuations. Wiley & Sons, New York, 1977.
7. A. S. Pikovsky . Spatial development of chaos in nonlinear media. Phys. Lett. A, 137 (1989), 121-127
8. A. Pikovsky , O. Popovych . Persistent patterns in deterministic mixing flows. Europhys. Lett., 61 (2003), 625-631 (Pubitemid 36316707)
9. L. Pismen. Patterns and interfaces in dissipative dynamics. Springer, Berlin, 2006.
10. D. Rothstein , E. Henry , J. P. Gollub . Persistent patterns in transient chaotic fluid mixing. Nature, 401 (1999), 770-772
11. A. B. Rovinsky , M. Menzinger . Differential flow instability in dynamical systems without an unstable (activator) subsystem. Phys. Rev. Lett., 72(1994), 2017-2020 (Pubitemid 24975082)
12. A. Straube , M. Abel , A. Pikovsky . Temporal chaos versus spatial mixing in reaction-advection-diffusion systems. Phys. Rev. Lett., 93(2004), 174501
13. T. Tl , A. de Moura , C. Grebogi , G. Krolyi . Chemical and biological activity in open flows: a dynamical system approach. Physics Reports, 413(2005), 91-196 (Pubitemid 40721458)
14. A. M. Turing . The chemical basis of morphogenesis, Philos. Trans. Roy. Soc. London, Ser. B 237(1952), 37-72.
15. D. A. Vasquez Chemical instability induced by a shear flow. Phys. Rev. Lett., 93 (2004), 104501
16. V. Z. Yakhnin , A. B. Rovinsky , M. Menzinger . Convective instability induced by differential transport in the tubular packed-bed reactor. Chemical Engineering Science, 50(1995), 2853-2859