Manipulation of self-aggregation patterns and waves in a reaction-diffusion system by optimal boundary control strategies

Physical Review Letters

Volumn 91, Issue 20, 2003, Pages

  Lebiedz, Dirk ^a   Brandt Pollmann, Ulrich ^a  

^a UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

AGGLOMERATION; BACTERIA; DIFFUSION; REACTION KINETICS; WAVE PROPAGATION;

OPTIMAL BOUNDARY CONTROL STRATEGIES; REACTION DIFFUSION SYSTEM; SELF AGGREGATION PATTERNS;

PHYSICS;

EID: 0346846623     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.91.208301     Document Type: Article

References (30)

1. P. Ball, The Self-Made Tapestry: Pattern Formation in Nature (Oxford University Press, Oxford, 1998).
2. D. Walgraef, Spatio-Temporal Pattern Formation, With Examples from Physics, Chemistry, and Materials Science (Springer-Verlag, New York, 1996).
3. G. Nicolis and I. Prigogine, Self-organization in Nonequilibrium Systems (Wiley, New York, 1977).
4. J. Wolff, A. Papathanasiou, I. Kevrekidis, H. Rotermund, and G. Ertl, Science 294, 134 (2001).10.1126/science.1063597
5. M. Kim, M. Bertram, M. Pollmann, A. von Oertzen, A. Mikhailov, H. Rotermund, and G. Ertl, Science 292, 1357 (2001).10.1126/science.1059478
6. T. Shinbrot, C. Grebogi, E. Ott, and J. Yorke, Nature (London) 363, 411 (1993).10.1038/363411a0
7. T. Sakurai, E. Mihaliuk, F. Chirila, and K. Showalter, Science 296, 2009 (2002).10.1126/science.1071265
8. E. Mihaliuk, T. Sakurai, F. Chirila, and K. Showalter, Faraday Discuss.FDISE6 120, 383 (2001).
9. V. Vanag, L. Yang, M. Dolnik, A. Zhabotinsky, and I. Epstein, Nature (London) 406, 389 (2000).10.1038/35019038
10. S. Sinha and N. Gupte, Phys. Rev. EPLEEE8 58, R5221 (1998).10.1103/PhysRevE.58.R5221
11. S. Sinha and N. Gupte, Phys. Rev. EPLEEE8 64, 015203(R) (2001).10.1103/PhysRevE.64.015203
12. G. Osipov, B. Shulgin, and J. Collins, Phys. Rev. EPLEEE8 58, 6955 (1998).10.1103/PhysRevE.58.6955
13. J. Xiao, G. Hu, and J. Gao, Int. J. Bifurcation Chaos Appl. Sci. Eng.IJBEE4 10, 655 (2000).10.1016/S0218-1274(00)00045-1
14. A. Pertsov, J. Davidenko, R. Salomonsz, W. Baxter, and J. Jalife, Circ. Res. 72, 631 (1993).
15. R. Martin, G.-L. Oppo, G. Harkness, A. Scroggie, and W. Firth, Opt. Express 1, 39 (1997).
16. R. Tyson, S. Lubkin, and J. Murray, J. Math. Biol. 38, 359 (1999).10.1007/s002850050153
17. R. Tyson, L. Stern, and R. LeVeque, J. Math. Biol. 41, 455 (2000).10.1007/s002850000038
18. B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walter, Molecular Biology of the Cell (Garland Science, New York, 2002).
19. H. Othmer and T. Hillen, SIAM J. Appl. Math. 62, 1222 (2002).10.1137/S0036139900382772
20. H. Berg and L. Turner, Biophys. J. 58, 919 (1990).
21. E. Budrene and H. Berg, Nature (London) 349, 630 (1991).10.1038/349630a0
22. E. Budrene and H. Berg, Nature (London) 376, 49 (1995).10.1038/376049a0
23. D. Leineweber, I. Bauer, H. Bock, and J. Schlöder, Comput. Chem. Eng. 27, 157 (2003).10.1016/S0098-1354(02)00158-8
24. H. Bock and K. Plitt, in Proceedings of the Ninth IFAC World Congress, Budapest (Pergamon, Oxford, 1984).
25. A. Carbone, M. Gronov, M. Gronov, and P. Prusinkiewicz, Pattern Formation in Biology, Vision and Dynamics (World Scientific, Singapore, 2000).
26. H. Kitano, Foundations of Systems Biology (MIT Press, Cambridge, 2001).
27. H. Kitano, Science 295, 1662 (2002).10.1126/science.1069492
28. H. Kitano, Nature (London) 420, 206 (2002).10.1038/nature01254
29. M. Diehl, H. Bock, J. Schlöder, R. Findeisen, Z. Nagy, and F. Allgöwer, J. Process Control 12, 577 (2002).10.1016/S0959-1524(01)00023-3
30. M. Morari and J. Lee, Comput. Chem. Eng. 23, 667 (1999).10.1016/S0098-1354(98)00301-9