Spatio-Temporal Pattern Formation

1. Front Matter

   Pages i-x

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2. Introduction

   • Daniel Walgraef

   Pages 1-13

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3. Instabilities and Patterns in Hydrodynamical Systems

   • Daniel Walgraef

   Pages 15-24

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4. Instabilities and Patterns in Reaction-Diffusion Systems

   • Daniel Walgraef

   Pages 25-36

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5. Generic Aspects of Pattern-Forming Instabilities

   • Daniel Walgraef

   Pages 37-64

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6. The Hopf Bifurcation and Related Spatio-Temporal Patterns

   • Daniel Walgraef

   Pages 65-85

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7. The Turing Instability and Associated Spatial Structures

   • Daniel Walgraef

   Pages 87-106

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8. Defects and Defect Bifurcations

   • Daniel Walgraef

   Pages 107-126

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9. The Effect of External Fields

   • Daniel Walgraef

   Pages 127-167

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10. Fronts

    • Daniel Walgraef

    Pages 169-187

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11. Pattern Formation: Generic versus Nongeneric Aspects

    • Daniel Walgraef

    Pages 189-196

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12. Microstructures in Irradiated Materials

    • Daniel Walgraef

    Pages 197-229

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13. Plastic Instabilities

    • Daniel Walgraef

    Pages 231-239

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14. Afterword

    • Daniel Walgraef

    Pages 241-244

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15. Appendices

    • Daniel Walgraef

    Pages 245-301

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16. Back Matter

    Pages 303-306

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Spatio-temporal patterns appear almost everywhere in nature, and their description and understanding still raise important and basic questions. However, if one looks back 20 or 30 years, definite progress has been made in the modeling of insta­ bilities, analysis of the dynamics in their vicinity, pattern formation and stability, quantitative experimental and numerical analysis of patterns, and so on. Universal behaviors of complex systems close to instabilities have been determined, leading to the wide interdisciplinarity of a field that is now referred to as nonlinear science or science of complexity, and in which initial concepts of dissipative structures or synergetics are deeply rooted. In pioneering domains related to hydrodynamics or chemical instabilities, the interactions between experimentalists and theoreticians, sometimes on a daily basis, have been a key to progress. Everyone in the field praises the role played by the interactions and permanent feedbacks between ex­ perimental, numerical, and analytical studies in the achievements obtained during these years. Many aspects of convective patterns in normal fluids, binary mixtures or liquid crystals are now understood and described in this framework. The generic pres­ ence of defects in extended systems is now well established and has induced new developments in the physics of laser with large Fresnel numbers. Last but not least, almost 40 years after his celebrated paper, Turing structures have finally been ob­ tained in real-life chemical reactors, triggering anew intense activity in the field of reaction-diffusion systems.

• deformation
• equation
• instability
• plastic deformation
• stability

• Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Bruxelles, Belgium

  Daniel Walgraef

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