메뉴 건너뛰기




Volumn 61, Issue 2, 2000, Pages 387-431

Chemical turing pattern formation analyses: Comparison of theory with experiment

Author keywords

Dissipative structures; Nonlinear stability analyses; Pattern formation; Reaction diffusion equations

Indexed keywords

GELS; NUMERICAL ANALYSIS; SOLIDIFICATION; STABILITY;

EID: 0343807197     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139997326211     Document Type: Review
Times cited : (32)

References (55)
  • 1
    • 0002695132 scopus 로고
    • Turing patterns: Myth to reality
    • R. Kapral and K. Showalter, eds., Kluwer, Dordrecht, The Netherlands
    • J. BOISSONADE, E. DULOS, AND P. DE KEPPER (1995), Turing patterns: Myth to reality, in Chemical Waves and Patterns, R. Kapral and K. Showalter, eds., Kluwer, Dordrecht, The Netherlands, pp. 221-268.
    • (1995) Chemical Waves and Patterns , pp. 221-268
    • Boissonade, J.1    Dulos, E.2    De Kepper, P.3
  • 2
    • 0000971882 scopus 로고
    • Turing bifurcations and pattern selection
    • R. Kapral and K. Showalter, eds., Kluwer, Dordrecht, The Netherlands
    • P. BORCKMANS, G. DEWEL, A DEWIT, AND D. WALGRAFF (1995), Turing bifurcations and pattern selection, in Chemical Waves and Patterns, R. Kapral and K. Showalter, eds., Kluwer, Dordrecht, The Netherlands, pp. 323-363.
    • (1995) Chemical Waves and Patterns , pp. 323-363
    • Borckmans, P.1    Dewel, G.2    Dewit, A.3    Walgraff, D.4
  • 3
    • 5544250703 scopus 로고
    • Experimental evidence of a sustained standing Turing-type nonequilibrium chemical pattern
    • V. CASTETS, E. DULOS, J. BOISSONADE, AND P. DE KEPPER (1990), Experimental evidence of a sustained standing Turing-type nonequilibrium chemical pattern, Phys. Rev. Lett., 64, pp. 2953-2956.
    • (1990) Phys. Rev. Lett. , vol.64 , pp. 2953-2956
    • Castets, V.1    Dulos, E.2    Boissonade, J.3    De Kepper, P.4
  • 4
    • 0005728268 scopus 로고
    • Morphological stability
    • D. T. J. Hurle, ed., Elsevier, Amsterdam
    • S. R. CORIELL AND G. B. MCFADDEN (1993), Morphological stability, in Handbook of Crystal Growth, Vol. 1, D. T. J. Hurle, ed., Elsevier, Amsterdam, pp. 785-858.
    • (1993) Handbook of Crystal Growth , vol.1 , pp. 785-858
    • Coriell, S.R.1    Mcfadden, G.B.2
  • 5
    • 12044252828 scopus 로고
    • Pattern formation outside of equilibrium
    • M. C. CROSS AND P. C. HOHENBERG (1993), Pattern formation outside of equilibrium, Rev. Modern Phys., 65, pp. 851-1112.
    • (1993) Rev. Modern Phys. , vol.65 , pp. 851-1112
    • Cross, M.C.1    Hohenberg, P.C.2
  • 6
    • 0023249062 scopus 로고
    • Thermocapillary instabilities
    • S. H. DAVIS (1987), Thermocapillary instabilities, Ann. Rev. Fluid Mech., 19, pp. 403-435.
    • (1987) Ann. Rev. Fluid Mech. , vol.19 , pp. 403-435
    • Davis, S.H.1
  • 7
    • 44949270147 scopus 로고
    • Turing-type chemical patterns in the chlorite-iodide-malonic acid reaction
    • P. DE KEPPER, V. CASTETS, E. DULOS, AND J. BOISSONADE (1991), Turing-type chemical patterns in the chlorite-iodide-malonic acid reaction, Phys. D, 49, pp. 161-169.
    • (1991) Phys. D , vol.49 , pp. 161-169
    • De Kepper, P.1    Castets, V.2    Dulos, E.3    Boissonade, J.4
  • 9
    • 36449007762 scopus 로고
    • Conventional and unconventional Turing patterns
    • V. DUFIET AND J. BOISSONADE (1992), Conventional and unconventional Turing patterns, J. Chem. Phys., 96, pp. 664-672.
    • (1992) J. Chem. Phys. , vol.96 , pp. 664-672
    • Dufiet, V.1    Boissonade, J.2
  • 10
    • 0000934296 scopus 로고
    • Pattern formation in large-scale Marangoni convection with deformable interface
    • A. A. GOLOVIN, A. A. NEPOMNYASHCHY, AND L. M. PISMEN (1995), Pattern formation in large-scale Marangoni convection with deformable interface, Phys. D, 81, pp. 117-147.
    • (1995) Phys. D , vol.81 , pp. 117-147
    • Golovin, A.A.1    Nepomnyashchy, A.A.2    Pismen, L.M.3
  • 11
    • 0021390252 scopus 로고
    • Symmetries and pattern selection in Rayleigh-Bénard convection
    • M. GOLUBITSKY, J. K. SWIFT, AND E. KNOBLICH (1984), Symmetries and pattern selection in Rayleigh-Bénard convection, Phys. D, 10, pp. 249-276.
    • (1984) Phys. D , vol.10 , pp. 249-276
    • Golubitsky, M.1    Swift, J.K.2    Knoblich, E.3
  • 13
    • 24544442979 scopus 로고
    • Pattern formation in the presence of symmetries
    • G. H. GUNARATNE, Q. OUYANG, AND H. L. SWINNEY (1994), Pattern formation in the presence of symmetries, Phys. Rev. E, 50, pp. 2802-2820.
    • (1994) Phys. Rev. E , vol.50 , pp. 2802-2820
    • Gunaratne, G.H.1    Ouyang, Q.2    Swinney, H.L.3
  • 15
    • 0343974367 scopus 로고
    • Pattern Selection with Anisotropy during Directional Solidification
    • Northwestern University, Evanston, IL
    • R. B. HOYLE, G. B. MCFADDEN, AND S. H. DAVIS (1995), Pattern Selection with Anisotropy During Directional Solidification, Appl. Math. Tech., Report 9404, Northwestern University, Evanston, IL.
    • (1995) Appl. Math. Tech., Report 9404
    • Hoyle, R.B.1    Mcfadden, G.B.2    Davis, S.H.3
  • 17
    • 0029163545 scopus 로고
    • A reaction-diffusion wave on the skin of the marine angelfish, Pomacanthus
    • S. KONDO AND R. ASAI (1995), A reaction-diffusion wave on the skin of the marine angelfish, Pomacanthus, Nature, 376, pp. 765-768.
    • (1995) Nature , vol.376 , pp. 765-768
    • Kondo, S.1    Asai, R.2
  • 19
    • 0343538564 scopus 로고
    • On roll, square, and hexagonal cellular flames
    • R. KUSKE AND B. J. MATKOWSKY (1994), On roll, square, and hexagonal cellular flames, European Appl. Math., 5, pp. 65-93.
    • (1994) European Appl. Math. , vol.5 , pp. 65-93
    • Kuske, R.1    Matkowsky, B.J.2
  • 20
    • 0001510852 scopus 로고
    • Existence of a hexagonal relief on the surface of a dielectric fluid in an external electric field
    • E. A. KUZNETSOV AND M. D. SPEKTOR (1976), Existence of a hexagonal relief on the surface of a dielectric fluid in an external electric field, Soviet Phys. JETP, 44, pp. 136-141.
    • (1976) Soviet Phys. JETP , vol.44 , pp. 136-141
    • Kuznetsov, E.A.1    Spektor, M.D.2
  • 21
    • 12044256206 scopus 로고
    • Modeling of Turing structures in the chlorite-iodide-malonic acid-starch reaction system
    • I. LENGYEL AND I. R. EPSTEIN (1991), Modeling of Turing structures in the chlorite-iodide-malonic acid-starch reaction system, Science, 251, pp. 650-652.
    • (1991) Science , vol.251 , pp. 650-652
    • Lengyel, I.1    Epstein, I.R.2
  • 22
    • 0026575824 scopus 로고
    • A chemical approach to designing Turing patterns in reaction-diffusion systems
    • I. LENGYEL AND I. R. EPSTEIN (1992), A chemical approach to designing Turing patterns in reaction-diffusion systems, Proc. Natl. Acad. Sci. USA, 89, pp. 3977-3979.
    • (1992) Proc. Natl. Acad. Sci. USA , vol.89 , pp. 3977-3979
    • Lengyel, I.1    Epstein, I.R.2
  • 23
    • 0002053029 scopus 로고
    • The chemistry behind the first experimental chemical examples of Turing patterns
    • R. Kapral and K. Showalter, eds., Kluwer, Dordrecht, The Netherlands
    • I. LENGYEL AND I. R. EPSTEIN (1995), The chemistry behind the first experimental chemical examples of Turing patterns, in Chemical Waves and Patterns, R. Kapral and K. Showalter, eds., Kluwer, Dordrecht, The Netherlands, pp. 297-322.
    • (1995) Chemical Waves and Patterns , pp. 297-322
    • Lengyel, I.1    Epstein, I.R.2
  • 24
    • 0000206138 scopus 로고
    • Quasi-two-dimensional Turing patterns in an imposed gradient
    • I. LENGYEL, S. KÁDÁR, AND I. R. EPSTEIN (1992), Quasi-two-dimensional Turing patterns in an imposed gradient, Phys. Rev. Lett., 69, pp. 2729-2732.
    • (1992) Phys. Rev. Lett. , vol.69 , pp. 2729-2732
    • Lengyel, I.1    Kádár, S.2    Epstein, I.R.3
  • 25
    • 0000453635 scopus 로고
    • Transient Turing structures in a gradient-free closed system
    • 1993
    • I. LENGYEL, S. KÁDÁR, AND I. R. EPSTEIN (1993), Transient Turing structures in a gradient-free closed system, Science, 259 (1993), pp. 493-495.
    • (1993) Science , vol.259 , pp. 493-495
    • Lengyel, I.1    Kádár, S.2    Epstein, I.R.3
  • 26
    • 11944255633 scopus 로고
    • Batch oscillation in the reaction of chlorine dioxide with iodine and malonic acid
    • I. LENGYEL, G. RÁBAI, AND I. R. EPSTEIN (1990a), Batch oscillation in the reaction of chlorine dioxide with iodine and malonic acid, J. Amer. Chem. Soc., 112, pp. 4606-4607.
    • (1990) J. Amer. Chem. Soc. , vol.112 , pp. 4606-4607
    • Lengyel, I.1    Rábai, G.2    Epstein, I.R.3
  • 27
    • 0001676886 scopus 로고
    • Experimental and modeling study of oscillations in the chlorine dioxide-iodine-malonic acid reaction
    • I. LENGYEL, G. RÁBAI, AND I. R. EPSTEIN (1990b), Experimental and modeling study of oscillations in the chlorine dioxide-iodine-malonic acid reaction, J. Amer. Chem. Soc., 112, pp. 9104-9110.
    • (1990) J. Amer. Chem. Soc. , vol.112 , pp. 9104-9110
    • Lengyel, I.1    Rábai, G.2    Epstein, I.R.3
  • 29
    • 0029102341 scopus 로고
    • Dynamics of stripe formation
    • H. MEINHARDT (1995), Dynamics of stripe formation, Nature, 376, pp. 722-723.
    • (1995) Nature , vol.376 , pp. 722-723
    • Meinhardt, H.1
  • 30
    • 0008530148 scopus 로고
    • The development of cells during the solidification of a dilute Pb-Sb alloy
    • L. R. MORRIS AND W. C. WINEGARD (1969), The development of cells during the solidification of a dilute Pb-Sb alloy, J. Crystal Growth, 5, pp. 361-375.
    • (1969) J. Crystal Growth , vol.5 , pp. 361-375
    • Morris, L.R.1    Winegard, W.C.2
  • 32
    • 0038946525 scopus 로고
    • The dynamics and analysis of patterns
    • D. L. Stein, ed., Addison-Wesley, New York
    • A. C. NEWELL (1989), The dynamics and analysis of patterns, in Lectures in the Sciences of Complexity, D. L. Stein, ed., Addison-Wesley, New York, pp. 107-173.
    • (1989) Lectures in the Sciences of Complexity , pp. 107-173
    • Newell, A.C.1
  • 36
    • 0000579309 scopus 로고
    • Rhombic patterns: Broken hexagonal symmetries
    • Q. OUYANG, G. H. GUNARATNE, AND H. L. SWINNEY (1993), Rhombic patterns: Broken hexagonal symmetries, Chaos, 3, pp. 707-711.
    • (1993) Chaos , vol.3 , pp. 707-711
    • Ouyang, Q.1    Gunaratne, G.H.2    Swinney, H.L.3
  • 37
    • 36449002257 scopus 로고
    • Dependence of Turing pattern wavelength on diffusion rate
    • Q. OUYANG, R. LI, G. LI, AND H. L. SWINNEY (1995), Dependence of Turing pattern wavelength on diffusion rate, J. Chem. Phys., 102, pp. 2551-2555.
    • (1995) J. Chem. Phys. , vol.102 , pp. 2551-2555
    • Ouyang, Q.1    Li, R.2    Li, G.3    Swinney, H.L.4
  • 38
    • 0000834042 scopus 로고
    • Spatial bistability of two-dimensional Turing patterns in a reaction-diffusion system
    • Q. OUYANG, Z. NOSZTICZIUS, AND H. L. SWINNEY (1992), Spatial bistability of two-dimensional Turing patterns in a reaction-diffusion system, J. Chem. Phys., 96, pp. 6773-6776.
    • (1992) J. Chem. Phys. , vol.96 , pp. 6773-6776
    • Ouyang, Q.1    Noszticzius, Z.2    Swinney, H.L.3
  • 39
    • 34047187677 scopus 로고
    • Transition from a uniform state to hexagonal and striped Turing patterns
    • Q. OUYANG AND H. L. SWINNEY (1991a), Transition from a uniform state to hexagonal and striped Turing patterns, Nature, 352, pp. 610-612.
    • (1991) Nature , vol.352 , pp. 610-612
    • Ouyang, Q.1    Swinney, H.L.2
  • 40
    • 0000494953 scopus 로고
    • Transition to chemical turbulence
    • Q. OUYANG AND H. L. SWINNEY (1991b), Transition to chemical turbulence, Chaos, 1, pp. 411-420.
    • (1991) Chaos , vol.1 , pp. 411-420
    • Ouyang, Q.1    Swinney, H.L.2
  • 41
    • 0001687033 scopus 로고
    • Onset and beyond Turing pattern formation
    • R. Kapral and K. Showalter, eds., Kluwer, Dordrecht, The Netherlands
    • Q. OUYANG AND H. L. SWINNEY (1995), Onset and beyond Turing pattern formation, in Chemical Waves and Patterns, R. Kapral and K. Showalter, eds., Kluwer, Dordrecht, The Netherlands, pp. 269-295.
    • (1995) Chemical Waves and Patterns , pp. 269-295
    • Ouyang, Q.1    Swinney, H.L.2
  • 42
    • 0016428438 scopus 로고
    • Nonlinear thermal convention
    • B. PALM (1975), Nonlinear thermal convention, Ann. Rev. Fluid Mech., 7, pp. 39-61.
    • (1975) Ann. Rev. Fluid Mech. , vol.7 , pp. 39-61
    • Palm, B.1
  • 43
    • 0343974358 scopus 로고
    • Pattern formation in a (2 + 1)-species activator-inhibitor-immobilizer system
    • J. E. PEARSON (1992), Pattern formation in a (2 + 1)-species activator-inhibitor-immobilizer system, Phys. A, 188, pp. 178-189.
    • (1992) Phys. A , vol.188 , pp. 178-189
    • Pearson, J.E.1
  • 44
    • 0000463357 scopus 로고
    • Interaction of Hopf and Turing bifurcations in chemical systems
    • A. ROVINSKY AND M. MENZINGER (1992), Interaction of Hopf and Turing bifurcations in chemical systems, Phys. Rev. A, 46, pp. 6315-6322.
    • (1992) Phys. Rev. A , vol.46 , pp. 6315-6322
    • Rovinsky, A.1    Menzinger, M.2
  • 45
    • 0018784247 scopus 로고
    • Simple chemical reaction systems with limit cycle behavior
    • J. SCHNACKENBERG (1979), Simple chemical reaction systems with limit cycle behavior, J. Theoret. Biol., 81, pp. 389-400.
    • (1979) J. Theoret. Biol. , vol.81 , pp. 389-400
    • Schnackenberg, J.1
  • 46
    • 0007175892 scopus 로고
    • The nonlinear interaction of a finite number of disturbances in a layer of fluid heated from below
    • L. A. SEGEL (1965), The nonlinear interaction of a finite number of disturbances in a layer of fluid heated from below, J. Fluid Mech., 21, pp. 359-384.
    • (1965) J. Fluid Mech. , vol.21 , pp. 359-384
    • Segel, L.A.1
  • 47
    • 0041115507 scopus 로고
    • A theoretical investigation of the development of interfacial cells during the solidification of a dilute binary alloy: Comparison with the experiments of Morris and Winegard
    • R. SRIRANGANATHAN, D. J. WOLLKIND, AND D. B. OULTON (1983), A theoretical investigation of the development of interfacial cells during the solidification of a dilute binary alloy: Comparison with the experiments of Morris and Winegard, J. Crystal Growth, 62, pp. 265-283.
    • (1983) J. Crystal Growth , vol.62 , pp. 265-283
    • Sriranganathan, R.1    Wollkind, D.J.2    Oulton, D.B.3
  • 48
    • 0342668345 scopus 로고
    • Weakly nonlinear stability analyses of one-dimensional Turing pattern formation in activator-inhibitor/immobilizer model systems
    • L. E. STEPHENSON AND D. J. WOLLKIND (1995), Weakly nonlinear stability analyses of one-dimensional Turing pattern formation in activator-inhibitor/immobilizer model systems, J. Math. Biol., 33, pp. 771-815.
    • (1995) J. Math. Biol. , vol.33 , pp. 771-815
    • Stephenson, L.E.1    Wollkind, D.J.2
  • 49
    • 0029137901 scopus 로고
    • Surface-tension-driven Bénard convection at infinite Prandtl number
    • A. THESS AND S. A. ORSZAG (1995), Surface-tension-driven Bénard convection at infinite Prandtl number, J. Fluid Mech., 283, pp. 201-230.
    • (1995) J. Fluid Mech. , vol.283 , pp. 201-230
    • Thess, A.1    Orszag, S.A.2
  • 50
    • 0002011401 scopus 로고
    • The chemical basis of morphogenesis
    • A. M. TURING (1952), The chemical basis of morphogenesis, Philos. Trans. Roy. Soc. Lond., B237, pp. 37-72.
    • (1952) Philos. Trans. Roy. Soc. Lond. , vol.B237 , pp. 37-72
    • Turing, A.M.1
  • 52
    • 0343102623 scopus 로고
    • A new prototype problem for nonlinear stability theory: Plane-front alloy solidification versus free-surface Bénard convection
    • J. E. Flaherty and D. A. Drew, eds., SIAM, Philadelphia
    • D. J. WOLLKIND (1986), A new prototype problem for nonlinear stability theory: Plane-front alloy solidification versus free-surface Bénard convection, in Mathematics Applied to Fluid Mechanics and Stability, J. E. Flaherty and D. A. Drew, eds., SIAM, Philadelphia, pp. 205-217.
    • (1986) Mathematics Applied to Fluid Mechanics and Stability , pp. 205-217
    • Wollkind, D.J.1
  • 53
    • 0028449003 scopus 로고
    • Weakly nonlinear stability analyses of prototype reaction-diffusion model equations
    • D. J. WOLLKIND, V. S. MANORANJAN, AND L. ZHANG (1994), Weakly nonlinear stability analyses of prototype reaction-diffusion model equations, SIAM Rev., 36, pp. 176-214.
    • (1994) SIAM Rev. , vol.36 , pp. 176-214
    • Wollkind, D.J.1    Manoranjan, V.S.2    Zhang, L.3
  • 54
    • 0021385706 scopus 로고
    • A nonlinear stability analysis of a model equation for alloy solidification
    • D. J. WOLLKIND, D. B. OULTON, AND R. SRIRANGANATHAN (1984a), A nonlinear stability analysis of a model equation for alloy solidification, J. Physique, 45, pp. 505-516.
    • (1984) J. Physique , vol.45 , pp. 505-516
    • Wollkind, D.J.1    Oulton, D.B.2    Sriranganathan, R.3
  • 55
    • 0020779399 scopus 로고
    • Interfacial patterns during plane front alloy solidification
    • D. J. WOLLKIND, R. SRIRANGANATHAN, AND D. B. OULTON (1984b), Interfacial patterns during plane front alloy solidification, Phys. D, 12, pp. 215-240.
    • (1984) Phys. D , vol.12 , pp. 215-240
    • Wollkind, D.J.1    Sriranganathan, R.2    Oulton, D.B.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.