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Max‐Planck‐Medaille: One Hundred Years of Nonequilibrium Patterns
Author(s) -
Hohenberg Pierre
Publication year - 1999
Publication title -
physikalische blätter
Language(s) - English
Resource type - Journals
eISSN - 1521-3722
pISSN - 0031-9279
DOI - 10.1002/phbl.19990550710
Subject(s) - instability , non equilibrium thermodynamics , physics , convection , statistical physics , homogeneous , parameter space , amplitude , pattern formation , front (military) , space (punctuation) , steady state (chemistry) , classical mechanics , mechanics , mathematics , thermodynamics , geometry , quantum mechanics , meteorology , linguistics , philosophy , genetics , chemistry , biology
Among the simplest macroscopic nonequilibrium systems are spatially uniform ones in which energy is fed in at a steady or periodic rate. An example is a horizontal layer of fluid heated from below (Rayleigh‐Bénard convection) for which the control parameter R , describing the rate at which energy is fed into the system, is the temperature difference between the top and bottom plates of the layer. In a typical scenario the system remains uniform for small R , but the homogeneous state undergoes a linear instability at a critical value R c , above which a spatial pattern emerges and grows. Initially this pattern is often spatially regular and either stationary or periodic in time. As R increases new instabilities and patterns occur, with increasing manifestations of disorder in space and time. Near the linear instability it can be shown that the system obeys universal “amplitude equations” or “Ginzburg‐Landau equations” whose solutions show many features in common with experimental systems. Examples of regular and irregular phenomena that will be discussed include pattern selection, front propagation, and spatiotemporal chaos.