Book contents
- Frontmatter
- Contents
- preface
- 1 Self-organized and self-assembled structures
- 2 Order parameter, free energy, and phase transitions
- 3 Free energy functional
- 4 Phase separation kinetics
- 5 Langevin model for nonconserved order parameter systems
- 6 Langevin model for conserved order parameter systems
- 7 Interface dynamics at late times
- 8 Domain growth and structure factor for model B
- 9 Order parameter correlation function
- 10 Vector order parameter and topological defects
- 11 Liquid crystals
- 12 Lifshitz–Slyozov–Wagner theory
- 13 Systems with long-range repulsive interactions
- 14 Kinetics of systems with competing interactions
- 15 Competing interactions and defect dynamics
- 16 Diffusively rough interfaces
- 17 Morphological instability in solid films
- 18 Propagating chemical fronts
- 19 Transverse front instabilities
- 20 Cubic autocatalytic fronts
- 21 Competing interactions and front repulsion
- 22 Labyrinthine patterns in chemical systems
- 23 Turing patterns
- 24 Excitable media
- 25 Oscillatory media and complex Ginzburg–Landau equation
- 26 Spiral waves and defect turbulence
- 27 Complex oscillatory and chaotic media
- 28 Resonantly forced oscillatory media
- 29 Nonequilibrium patterns in laser-induced melting
- 30 Reaction dynamics and phase segregation
- 31 Active materials
- References
- Index
24 - Excitable media
Published online by Cambridge University Press: 10 February 2010
- Frontmatter
- Contents
- preface
- 1 Self-organized and self-assembled structures
- 2 Order parameter, free energy, and phase transitions
- 3 Free energy functional
- 4 Phase separation kinetics
- 5 Langevin model for nonconserved order parameter systems
- 6 Langevin model for conserved order parameter systems
- 7 Interface dynamics at late times
- 8 Domain growth and structure factor for model B
- 9 Order parameter correlation function
- 10 Vector order parameter and topological defects
- 11 Liquid crystals
- 12 Lifshitz–Slyozov–Wagner theory
- 13 Systems with long-range repulsive interactions
- 14 Kinetics of systems with competing interactions
- 15 Competing interactions and defect dynamics
- 16 Diffusively rough interfaces
- 17 Morphological instability in solid films
- 18 Propagating chemical fronts
- 19 Transverse front instabilities
- 20 Cubic autocatalytic fronts
- 21 Competing interactions and front repulsion
- 22 Labyrinthine patterns in chemical systems
- 23 Turing patterns
- 24 Excitable media
- 25 Oscillatory media and complex Ginzburg–Landau equation
- 26 Spiral waves and defect turbulence
- 27 Complex oscillatory and chaotic media
- 28 Resonantly forced oscillatory media
- 29 Nonequilibrium patterns in laser-induced melting
- 30 Reaction dynamics and phase segregation
- 31 Active materials
- References
- Index
Summary
Excitable media are spatially distributed systems with a stable state that responds to perturbations in a distinctive way. If the normal resting state of the medium is perturbed sufficiently strongly, the perturbation is amplified before the system returns to the resting state. Such excitable media are commonly found in nature, and self-organized wave patterns in these systems control the behavior of many physical and biological systems (Zykov, 1987; Mikhailov, 1994; Kapral and Showalter, 1995). Surface catalytic oxidation reactions often proceed through the propagation of excitable waves of oxidation that sweep across the surface of the catalyst. The oxidation of CO on Pt surfaces has been especially well studied in this context (Ertl, 2000). In biological systems waves of this type occur in the aggregation stage of the slime mould Dictyostelium discoideum, where the chemical signaling is through periodic waves of cAMP; also, the Ca+2 waves in systems such as Xenopus laevis oocytes and pancreatic β cells fall into this category (Goldbeter, 1996). Electrochemical waves in cardiac and nerve tissue also depend on the excitability of the medium, and the appearance and/or breakup of spiral wave patterns (Fig. 24.1) are believed to be responsible for various types of arrhythmia in the heart (Winfree, 1987; Fenton et al., 2002; Clayton and Holden, 2004). Excitable waves have been extensively studied (Belmonte et al., 1997) for the BZ reaction, one of the first systems in which such waves were observed (Zaikin and Zhabotinsky, 1970; Winfree, 1972). Chemical waves in excitable media often take the form of spirals, and Fig. 24.2 shows spiral waves in the Belousov–Zhabotinsky reaction under conditions where this chemical medium is excitable.
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- Dynamics of Self-Organized and Self-Assembled Structures , pp. 212 - 231Publisher: Cambridge University PressPrint publication year: 2009