Lecture 8
- Detailed notes on the amplitude equation approach
- Notes on the multiple-scales perturbation method
- References to related papers
- Java demonstrations
- Eckhaus instability
- Zigzag instability
- Swift-Hohenberg equation: stripes
- Swift-Hohenberg equation: hexagons
- Lecture 9
- Notes on the phase equation
- Paper by Wesfried and Croquette on experimental test of the phase diffusion equation in convection [Phys. Rev. Lett. 45, 634 (1980)]
- A review article The topological theory of defects in ordered media
Rev. Mod. Phys. 51, 591 (1979) by Mermin discusses the mathematical theory of topological defects in ordered system. This discussion applies to both equilibrium and nonequilibrium systems.
- A review article The world of the complex Ginzburg-Landau equation Rev. Mod. Phys. 74, 99 (2002)
by Aranson and Kramer provides a comprehensive discussion of the Complex Ginzburg-Landau equation
- Java demonstrations
- Complex Ginzburg-Landau equation
- Complex Ginzburg-Landau equation (larger system)
- Nonlinear waves in a reaction diffusion system
- Lecture 10
- Java demonstrations
- References
- General
- Mathematical Biology by J. D. Murray, Springer-Verlag (1989)
- Models of Biological Pattern Formation by H. Meinhardt, Academic (1992)
- The Algorithmic Beauty of Sea Shells, H. Meinhardt, Springer (1995)
- Pattern Formation Outside of Equilibrium, M.C. Cross and P.C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993), Section XI
- Turing Patterns
- The Chemical Basis of Morphogenesis, A. M. Turing, Phil. Trans. Roy. Soc. Lon. 237, (1952)
- Transition from a Uniform State to Hexagonal and Striped Turing Patterns Patterns, Q. Ouyang and H. L. Swinney, Nature 352, 610 (1991)
- Transition to Chemical Turbulence, Q. Ouyang and H. L. Swinney, Chaos 1, 411 (1991)
- Segmentation in Drosophila
- Mechanism of Eve Stripe Formation, J. Reinitz and D. H. Sharp, Mechanisms of Development 49, 133 (1995)
- Establishment of Developmental Precision and Proportions in the Early Drosophila Embryo, B. Houchmandzadeh, E. Wieschaus and S. Leibler, Nature 415, 798 (2002)
- Dynamical Modelling of Pattern Formation During Embryonic Development, D. Thieffry and L. Sanchez,
Current Opinion in Genetics & Development 13, 326 (2003)
- The FlyEx database
- Fish Patterns
- A Reaction-Diffusion Wave on the Skin of the Marine Angelfish Pomacanthus, S. Kondo and R. Asai,
Nature 376, 765 (1995)
- Reaction and Diffusion on Growing Domains: Scenarios for Robust Pattern Formation, E. J. Crampin, E. A. Gaffney, and P. K. Maini, Bull. Math. Biology 61, 1093 (1999)
- Patterns on the Visual Cortex
- Geometry of Orientation and Ocular Dominance Columns in Monkey Striate Cortex, K. Obermayer and G. Blasde, J. Neuroscience 13, 4114 (1993)
- Orientation Preference Patterns in Mammalian Visual Cortex: a Wire Length Minimization Approach, A. A. Koulakov and D. B. Chklovskii, Neuron 29, 519 (2001)
- What Geometric Visual Hallucinations Tell Us about the Visual Cortex, P. C. Bressloff et al., Neural Computation 14, 473 (2002)
All files are in Acrobat (pdf) format
Last modified: 10 July, 2008, Michael Cross