Crystal growth as an excitable medium

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 370, Issue 1969, 2012, Pages 2866-2876

  Cartwright, Julyan H E ^a   Checa, Antonio G ^b   Escribano, Bruno ^c   Sainz Díazl, C Ignacio ^a  

^a INSTITUTO ANDALUZ DE CIENCIAS DE LA TIERRA   (Spain)

^b UNIVERSITY OF GRANADA   (Spain)

^c BCAM BASQUE CENTER FOR APPLIED MATHEMATICS   (Spain)

Author keywords

Crystal morphology; Defects; Growth models; Nucleation

Indexed keywords

BIOLOGICAL MATERIALS; DEFECTS; LIQUID CRYSTALS; NUCLEATION; SURFACE DEFECTS;

BIOLOGICAL LIQUIDS; CRYSTAL MORPHOLOGIES; CRYSTAL SURFACES; EXCITABLE MEDIA; EXCITABLE MEDIUM; GROWTH MODELS; LAYER GROWTH; PHYSICAL SYSTEMS; PHYSICS OF CRYSTAL GROWTH; SOLID CRYSTALS; TARGET PATTERNS; TWO-DIMENSIONAL NUCLEATION;

CRYSTAL GROWTH;

BIOPOLYMER; NANOMATERIAL;

ARTICLE; CHEMICAL MODEL; CHEMICAL STRUCTURE; CHEMISTRY; CRYSTALLIZATION; MACROMOLECULE; METHODOLOGY; ULTRASTRUCTURE;

BIOPOLYMERS; CRYSTALLIZATION; MACROMOLECULAR SUBSTANCES; MODELS, CHEMICAL; MODELS, MOLECULAR; NANOSTRUCTURES;

EID: 84861945569     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2011.0600     Document Type: Article

References (27)

1. Burton, W. K., Cabrera, N. & Frank, F. C. 1951 The growth of crystals and the equilibrium structure of their surfaces. Phil. Trans. R. Soc. Lond. A 243, 299-358. (doi:10.1098/rsta.1951.0006)
2. Ball, P. 2001 The self-made tapestry: pattern formation in nature. Cambridge, UK: Cambridge University Press.
3. Meron, E. 1992 Pattern formation in excitable media. Phys. Rep. 218, 1-66. (doi:10.1016/0370- 1573(92)90098-K)
4. Tyson, J. J. & Keener, J. P. 1988 Singular perturbation theory of traveling waves in excitable media (a review). Physica D. Nonlin. Phenom. 32, 327-361. (doi:10.1016/0167-2789(88)90062-0)
5. Feingold, M., Gonzalez, D. L., Piro, O. & Viturro, H. 1988 Phase locking, period doubling, and chaotic phenomena in externally driven excitable systems. Phys. Rev. A 37, 4060-4063. (doi:10.1103/PhysRevA.37.4060)
6. Cartwright, J. H. E., Hernández-García, E. & Piro, O. 1997 Burridge-Knopoff models as elastic excitable media, Phys. Rev. Lett. 79, 527-530. (doi:10.1103/PhysRevLett.79.527) (Pubitemid 127653663)
7. Cartwright, J. H. E., Eguiluz, V. M., Hernández-García, E. & Piro, O. 1999 Dynamics of elastic excitable media. Int. J. Bifurc. Chaos 9, 2197-2202. (doi:10.1142/S0218127499001620) (Pubitemid 129344674)
8. Cartwright, J. H. E. 2000 Emergent global oscillations in heterogeneous excitable media: the example of pancreatic beta cells. Phys. Rev. E 62, 1149-1154. (doi:10.1103/PhysRevE.62.1149)
9. Cartwright, J. H. E., Checa, A. G., Escribano, B. & Sainz-Díaz, C. I. 2009 Spiral and target patterns in bivalve nacre manifest a natural excitable medium from layer growth of a biological liquid crystal. Proc. Natl Acad. Sci. USA 106, 10 499-10 404. (doi:10.1073/pnas. 0900867106)
10. Chernov, A. 2003 Protein crystals and their growth. J. Struct. Biol. 142, 3-21. (doi:10.1016/ S1047-8477(03)00034-0) (Pubitemid 36469245)
11. McPherson, A., Kuznetsov, Y. G., Malkin, A. & Plomp, M. 2003 Macromolecular crystal growth as revealed by atomic force microscopy. J. Struct. Biol. 142, 32-46. (doi:10.1016/S1047- 8477(03)00036-4) (Pubitemid 36457888)
12. Faraday, M. 1834 Experimental researches in electricity. Sixth series. Phil. Trans. R. Soc. Lond. 124, 55-76. (doi:10.1098/rstl.1834.0007)
13. Mackay, A. L. 1976 Crystal symmetry. Phys. Bull. 27, 495-497.
14. Markus, M. & Hess, B. 1990 Isotropic cellular automaton for modelling excitable media. Nature 347, 56-58. (doi:10.1038/347056a0) (Pubitemid 120015016)
15. Burgers, J. M. 1940 Geometrical considerations concerning the structural irregularities to be assumed in a crystal. Proc. Phys. Soc. 52, 23-33. (doi:10.1088/0959-5309/52/1/304)
16. Shapere, A. & Wilczek, F. (eds) 1989 Geometric phases in physics. Singapore: World Scientific.
17. Frank, F. C. & Read, W. T. 1950 Multiplication processes for slow moving dislocations. Phys. Rev. 79, 722-723. (doi:10.1103/PhysRev.79.722)
18. Chernov, A. A. 2004 Notes on interface growth kinetics 50 years after Burton, Cabrera and Frank. J. Crystal Growth 264, 499-518. (doi:10.1016/j. jcrysgro.2003.12.076)
19. Falo, F., Bishop, A. R., Lomdahl, P. S. & Horovitz, B. 1991 Langevin molecular dynamics of interfaces: nucleation versus spiral growth. Phys. Rev. B 43, 8081-8088. (doi:10.1103/ PhysRevB.43.8081)
20. Aranson, I. S., Bishop, A. R., Daruka, I. & Vinokur, V. M. 1998 Ginzburg-Landau theory of spiral surface growth. Phys. Rev. Lett. 80, 1770-1773. (doi:10.1103/PhysRevLett.80.1770) (Pubitemid 128622994)
21. Smereka, P. 2000 Spiral crystal growth. Phys. D 138, 282-301. (doi:10.1016/S0167-2789(99)00216-X)
22. Uehara, T. & Sekerka, R. F. 2003 Phase field simulations of faceted growth for strong anisotropy of kinetic coefficient. J. Crystal Growth 254, 251-261. (doi:10.1016/S0022-0248(03)01120-5)
23. Chen, C. & Lan, C. 2009 Efficient adaptive three-dimensional phase-field simulation of dendritic crystal growth from various supercoolings using rescaling. J. Crystal Growth 311, 702-706. (doi:10.1016/j.jcrysgro.2008. 09.077)
24. Pimpinelli, A. & Villain, J. 1998 Physics of crystal growth. Cambridge, UK: Cambridge University Press.
25. Misbah, C., Pierre-Louis, O. & Saito, Y. 2010 Crystal surfaces in and out of equilibrium: a modern view. Rev. Mod. Phys. 82, 981. (doi:10.1103/RevModPhys.82.981)
26. Pina, C. M. & Rico-García, A. 2009 Nanoscale anglesite growth on the celestite (001) face. Surf. Sci. 603, 2708-2713. (doi:10.1016/j.susc. 2009.07.007)
27. Cartwright, J. H. E. & Checa, A. G. 2007 The dynamics of nacre self-assembly. J. R. Soc. Interface 4, 491-504. (doi:10.1098/rsif.2006.0188) (Pubitemid 46846678)