Finite size effects near the onset of the oscillatory instability

Nonlinearity

Volumn 9, Issue 5, 1996, Pages 1129-1171

  Martel, Carlos ^a   Vega, José M ^a  

^a UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000705004     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/9/5/005     Document Type: Article

References (67)

1. Cross M C and Hohenberg P C 1993 Pattern formation outside of equilibrium Rev. Mod. Phys. 65 851-1112
2. Steinberg V, Fineberg J, Moses E and Rehberg I 1989 Pattern selection and transition to turbulence in propagating waves Physica 37D 359-83
3. Bensimon D, Kolodner P, Surko C M, Williams H and Croquette V 1990 Competing and coexisting dynamical states of travelling-wave convection in an annulus J. Fluid Mech. 217 441-67
4. Kolodner P 1993 Repeated transients of weakly nonlinear travelling-wave convection Phys. Rev. E 47 1038-48
5. Kaplan E and Steinberg V 1993 Measurement of reflection of travelling waves near the onset of binary-fluid convection Phys. Rev. E 48 R661-4
6. Predtechensky A A, McCormick W D, Swift J B, Noszticzius Z and Swinney H L 1994 Onset of travelling waves in isothermal double diffusive convection Phys. Rev. Lett. 72 218-21
7. 4He J. Fluid Mech. 189 263-86
8. Croquette V and Williams H 1989 Nonlinear competition between waves on convective rolls Phys. Rev. A 39 2765-8
9. Croquette V and Williams H 1989 Nonlinear waves of the oscillatory instability on finite convective rolls Physica 37D 300-14
10. Andereck C D, Liu S S and Swinney H L 1986 Flow regimes in a circular Couette system with independently rotating cylinders J. Fluid Mech. 164 155-83
11. Tagg R, Edwards W S and Swinney H L 1990 Convective versus absolute instability in flow between counter-rotating cylinders Phys. Rev. A 42 831-7
12. Dubois M, Daviaud F, Ronsin O and Bergé P 1992 Traveling waves in pure fluids locally heated along wires Physica 61D 140-6
13. Vince J M and Dubois M 1992 Hot wire below the free surface of a liquid: structural and dynamical properties of a secondary instability Europhys. Lett. 20 505-10
14. Daviaud F and Vince J M 1993 Travelling waves in a fluid layer subjected to a horizontal temperature gradient Phys. Rev. E 48 4432-6
15. Joets A and Ribotta R 1988 Localized, time-dependent state in the convection of a nematic liquid crystal Phys. Rev. Lett. 60 2164-7
16. Rehberg I, Rasenat S and Steinberg V 1989 Travelling waves and defect-initiated turbulence in electroconvecting nematics Phys. Rev. Lett. 62 756-9
17. Rehberg I, Winkler B L, de la Torre M, Rasenat S and Schöpf W 1989 Pattern formation in a liquid crystal Advances in Solid State Physics vol 29, ed V Roessler (Braunschweig: Vieweg) pp 35-52
18. de la Torre M 1990 Contribución al estudio de la formación de estructuras en fluidos anisótropos Doctoral Thesis Universidad Nacional de Educación a Distancia, Madrid
19. Markstein G H 1964 Nonsteady Flame Propagation (New York: Plenum)
20. Ferguson C R and Keck J C 1979 Stand-off distances on a flat burner Combustion and Flame 34 85-98
21. Sabathier F, Boyer L and Clavin P 1979 Experimental study of weak turbulent premixed flames Combustion and Flame 35 139-53
22. Buckmaster J 1983 Stability of the porous plug burner flame SIAM J. Appl. Math. 43 1335-49
23. Margolis S B and Williams F A 1989 Diffusional-thermal instability of a solid propellant flame SIAM J. Appl. Math. 49 1390-420
24. Coullet P, Fauve S and Tirapegui E 1985 Large scale instability of nonlinear standing waves J. Physique Lett. 46 787-91
25. Hohenberg P C and Cross M C 1987 An introduction to pattern formation in non-equilibrium systems Lecture Notes in Physics vol 268 (Berlin: Springer)
26. Fauve S 1987 Large scale instabilities of cellular flows Instabilities and Non-equilibrium Structures ed E Tirapegui and D Villarroel (Dordrecht: Reidel)
27. Pierce R D and Knobloch E 1995 Asymptotically exact Zakharov equations and the stability of water waves with bimodal spectra Physica 81D 341-73
28. Christodoulides P and Dias F 1994 Resonant capillary-gravity interfacial waves J. Fluid Mech. 265 303-43
29. Nicolás J A, Martel C and Vega J M 1996 Weakly non-linear oscillations in liquid bridges under high-frequency axial forcing in preparation
30. Knobloch E and Gibbon J D 1991 Coupled NLS equations for counter propagating waves in systems with reflection symmetry Phys. Lett. 154A 353-6
31. Cross M C 1986 Travelling and standing waves in binary-fluid convection in finite geometries Phys. Rev. Lett. 57 2935-8
32. Cross M C 1988 Structure of nonlinear travelling waves in finite geometries Phys. Rev. A 38 3593-600
33. Cross M C 1989 Nonlinear travelling wave states in finite geometries Physica 37D 315-8
34. Cross M C and Kuo E Y 1992 One dimensional spatial structure near a Hopf bifurcation at finite wave number Physica 59D 90-120
35. Bensimon D, Kolodner P, Surko C M, Williams H and Croquette V 1990 Competing and coexisting dynamical states of travelling-wave convection in an annulus J. Fluid Mech. 217 441-67
36. Chikwendu S C and Kevorkian J 1972 A perturbation method for hyperbolic equations with small nonlinearities SIAM J. Appl. Math. 22 235-58
37. Knobloch E and de Luca J 1990 Amplitude equations for travelling wave convection Nonlinearity 3 575-80
38. Alvarez-Pereira C and Vega J M 1992 On the pulsating instability of two-dimensional flames Eur. J. Appl. Math. 3 55-73
39. Vega J M 1993 On the amplitude equations arising at the onset of the oscillatory instability in pattern formation SIAM J. Math. Anal. 24 603-17
40. Knobloch E 1992 Nonlocal amplitude equations Pattern Formation in Complex Dissipative Systems ed S Kai (Singapore: World Scientific)
41. Martel C 1995 La Inestabilidad Oscilatoria y sus Aplicaciones en Mecánica de Fluidos y Combustión Doctoral Thesis Universidad Politécnica de Madrid, Madrid
42. Martel C and Vega J M 1996 A non-local amplitude equation that applies at the oscillatory instability in finite geometries, in preparation
43. Martel C and Vega J M 1996 Global stability properties of a hyperbolic system arising in pattern formation Nonlinear Anal. TMA to appear
44. Martel C and Vega J M 1996 Dynamics of a hyperbolic system that applies at the onset of the oscillatory instability, in preparation
45. Knobloch E 1986 Oscillatory convection in binary mixtures Phys. Rev. A 34 1538-49
46. Dangelmayr G and Knobloch E 1987 The Physics of Structure Formation: Theory and Simulation ed W Güttinger and G Dangelmayr (Berlin: Springer)
47. Clever R M and Busse F H 1989 Nonlinear oscillatory convection in the presence of a vertical magnetic field J. Fluid Mech. 201 507-23
48. Schöpf W and Zimmermann W 1989 Multicritical behaviour in binary fluid convection Europhys. Lett. 8 41-6
49. Dangelmayr G, Knobloch E and Wegelin M 1991 Dynamics of travelling waves in finite containers Europhys. Lett. 16 723-9
50. Knobloch E and Silber M 1993 Oscillatory convection in a rotating layer Physica 63D 213-32
51. Kevorkian J and Cole J D 1981 Perturbation Methods in Applied Mathematics (Berlin: Springer)
52. Lagerstrom P A 1988 Matched Asymptotic Expansions (Berlin: Springer)
53. Roberts A J 1992 Boundary conditions for approximate differential equations J. Austral. Math. Soc. Ser. B 34 54-80
54. Jeffrey A and Kawahara T 1982 Asymptotic Methods in Nonlinear Wave Theory (Boston, MA: Pitman)
55. Coddington E A and Levinson N 1955 Theory of Ordinary Differential equations (New York: McGraw-Hill)
56. Gil L 1991 Space and time intermittency behaviour of a one-dimensional complex Ginzburg-Landau equation Nonlinearity 4 1213-22
57. Eidel'man S D 1969 Parabolic Systems (Amsterdam: North-Holland)
58. Teman R 1983 Navier-Stokes Equations and Nonlinear Functional Analysis (Society for Industrial and Applied Mathematics)
59. Clavin P 1985 Dynamic behaviour of premixed flame fronts in laminar and turbulent flows Prog. Energy Combust. Sci. 11 1-59
60. Jackson T L and Kapila A K 1986 Thermal expansion effects on perturbed premixed flames Reacting Flows: Combustion and Chemical Reactors (Lectures in Applied Mathematics 24-1) ed G S S Ludford (Providence, RI: American Mathematical Society) pp 325-48
61. Parra I E and Vega J M 1992 Multiple solutions of some semilinear elliptic equations in slender cylindrical domains J. Diff. Eqns 100 225-56
62. Dancer E N 1993 Weakly nonlinear Dirichlet problems on long or thin domains Mem. Am. Math. Soc. 105 501
63. Berestycki H and Nirenberg L 1990 Some qualitative properties of solutions of semilinear elliptic equations in cylindrical domains Analysis ... etc, Research Papers Published in Honor of Jürgen Moser's 60th Birthday ed P H Rabinowitz and E Zehnder (New York: Academic) pp 115-64
64. Vega J M 1993 The asymptotic behaviour of the solutions of some semilinear elliptic equations in cylindrical domains J. Diff. Eqns 102 119-52
65. Agmon S and Nirenberg L 1963 Properties of solutions of ordinary differential equations in Banach space Commun. Pure Appl. Math. 16 121-239
66. Pazy A 1967 Asymptotic expansion of solutions of ordinary differential equations in Hilbert space Arc. Rational Mech. Anal. 24 193-218
67. Simon L 1985 Isolated singularity of extrema of geometric variational problems Harmonic Mappings and Minimal Immersions (Lecture Notes in Mathematics 1161) ed E Giusti (Berlin: Springer)