Global feedback control of a long-wave morphological instability

Physica D: Nonlinear Phenomena

Volumn 199, Issue 1-2, 2004, Pages 61-81

  Nepomnyashchy, A A ^a,b   Golovin, A A ^b   Gubareva, V ^a   Panfilov, V ^c  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b NORTHWESTERN UNIVERSITY   (United States)

^c UNIVERSITY OF NEVADA   (United States)

Author keywords

Evolution equations; Feedback control; Morphological instability; Pattern formation

Indexed keywords

BOUNDARY CONDITIONS; CRYSTAL GROWTH; CRYSTALLIZATION; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; PROBLEM SOLVING; THERMAL EFFECTS;

CRYSTAL-MELT INTERFACE; EVOLUTION EQUATION; MORPHOLOGICAL INSTABILITY; PATTERN FORMATION;

FEEDBACK CONTROL;

EID: 9744263251     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2004.08.004     Document Type: Conference Paper

References (35)

1. S.H. Davis, Theory of Solidification, Cambridge University Press, Cambridge, 2001.
2. W.W. Mullins, R.F. Sekerka, Morphological stability of a particle growing by diffusion or heat flow, J. Appl. Phys. 34 (1963) 323-329.
3. W.W. Mullins, R.F. Sekerka, Stability of a planar interface during solidification of a dilute binary alloy, J. Appl. Phys. 35 (1964) 444-451.
4. T.P. Schultze, S.H. Davis, The influence of oscillatory and steady shears on interfacial stability during directional solidification, J. Cryst. Growth 143 (1994) 317-333.
5. T.P. Schultze, S.H. Davis, Shear stabilization of morphological instability during directional solidification, J. Cryst. Growth 149 (1995) 253-265.
6. Y.J. Chen, S.H. Davis, Directional solidification of a binary alloy into a cellular convective flow: localized morphologies, J. Fluid Mech. 395 (1999) 253-270.
7. T. Savina, A.A. Nepomnyashchy, S. Brandon, A.A. Golovin, D.R. Lewin, Feedback control of morphological instability, J. Cryst. Growth 237-239 (2002) 178-180.
8. T.V. Savina, A.A. Nepomnyashchy, S. Brandon, D.R. Lewin, A.A. Golovin, Suppressing morphological instability via feedback control, J. Cryst. Growth 240 (2002) 292-304.
9. J. Tang, H.H. Bau, Stabilization of the no-motion state in Rayleigh-Benard convection through the use of feedback-control, Phys. Rev. Lett. 70 (1993) 1795-1798.
10. L.E. Howle, Active control of Rayleigh-Benard convection, Phys. Fluids 9 (1997) 1861-1863.
11. J. Tang, H.H. Bau, Numerical investigation of the stabilization of the no-motion state of a fluid layer heated from below and cooled from above, Phys. Fluids 10 (1998) 1597-1610.
12. H.H. Bau, Control of Marangoni-Benard convection, Int. J. Heat Mass Transfer 42 (1999) 1327-1341.
13. R.O. Grigoriev, Contact line instability and pattern selection in thermally driven liquid films, Phys. Fluids 15 (2003) 1363-1374.
14. N. Gamier, R.O. Grigoriev, M.F. Schatz, Optical manipulation of microscale fluid flow, Phys. Rev. Lett. 91 (2003) 054501.
15. G. Hagen, I. Mezic, Spillover stabilization in finite-dimensional control and observer design for dissipative evolution equations, SIAM J. Contr. Optim. 42 (2003) 746-768.
16. A. Armaou, P.D. Christofides, Feedback control of the Kuramoto-Sivashinsky equation, Physica D 137 (2000) 49-61.
17. P. Kolodner, G. Flatgen, Spatial-feedback control of dispersive chaos in binary-fluid convection, Phys. Rev. E 61 (2000) 2519-2532.
18. K.A. Montgomery, M. Silber, Feedback control of traveling wave solutions of the complex Ginzburg-Landau equation, preprint.
19. D.J. Wollkind, L.A. Segel, Nonlinear stability analysis of freezing of a dilute binary alloy, Philos. Trans. R. Soc. A 268 (1970) 351-380.
20. G.I. Sivashinsky, On the cellular instability in the solidification of a dilute binary alloy, Physica D 8 (1983) 243-248.
21. A. Novick-Cohen, G.I. Sivashinsky, On the solidification front of a dilute binary alloy: thermal diffusivity effects and breathing solutions, Physica D 20 (1986) 237-258.
22. A.J. Bernoff, A.L. Bertozzi, Singularities in a modified Kuramoto-Sivashinsky equation describing interface motion for phase transition, Physica D 85 (1995) 375-404.
23. A.C. Or, R.E. Kelly, L. Cortelezzi, J.L. Speyer, Control of long-wavelength Marangoni-Benard convection, J. Fluid Mech. 387 (1999) 321-341.
24. U. Middya, D. Luss, M. Sheintuch, Impact of global interaction and symmetry on pattern selection and bifurcation, J. Chem. Phys. 101 (1994) 4688-4696.
25. V. Panfilov, M. Sheintuch, Using weighted global control for stabilizing patterned states, Chaos 9 (1999) 78-87.
26. V. Panfilov, M. Sheintuch, Control strategies for front stabilization in a tubular reactor model, AIChE J. 47 (2001) 187-196.
27. M. Bertram, A.S. Mikhailov, Pattern formation in a surface chemical reaction with global delayed feedback, Phys. Rev. E 63 (2001) 066102.
28. I.B. Simanovskii, A.A. Nepomnyashchy, Conective Instabilities in Systems with Interface, Gordon & Breach, Amsterdam, 1993.
29. I.S. Gradshteyn, I.M. Ryzhik, Tables of Integrals, Series and products, fourth ed., Academic Press, London, 1965.
30. A.C. Newell, J.A. Whitehead, Finite bandwidth, finite amplitude convection, J. Fluid Mech. 38 (1969) 279-303.
31. R.K. Dodd, J.C. Eilbeck, J.D. Gibbon, H.C. Morris, Solitons and Nonlinear Wave Equations, Academic Press, London, 1982.
32. F.H. Busse, The stability of finite amplitude cellular convection and its relation to an extremum principle, J. Fluid Mech. 30 (1967) 625-649.
33. A.A. Golovin, A.A. Nepomnyashchy, L.M. Pismen, Nonlinear evolution and secondary instabilities of Marangoni convection in a liquid-gas system with deformable interface, J. Fluid Mech. 341 (1997) 317-341.
34. G.H. Gunaratne, Q. Ouyang, H.L. Swinney, Pattern formation in the presence of symmetries, Phys. Rev. E 50 (1994) 2802-2820.
35. A.A. Golovin, A.A. Nepomnyashchy, L.M. Pismen, Non-potential effects in nonlinear dynamics of Marangoni convection, J. Bifurcation Chaos 12 (2002) 2487-2500.