The dynamics and analysis of patterns

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Patterns of an approximately periodic nature appear everywhere. One sees them in cloud formations, on the surface of the saguaro cactus, in the ripples of sand in deserts and near the edge of shallow water, in ocean gravity waves. These lectures are primarily directed toward patterns which arise when a system is driven away from some equilibrium state and undergoes sudden transitions which, with increasing external stress, break the symmetry of the simple, least stressed state, in more and more complicated ways. From such a series of bifurcations, one obtains organized structures which in some sense represent optimal configurations for the system at given values of its intrinsic parameters and the external stress parameter. 202For most of these lectures, we will use convection in fluids, either driven by temperature differences of by electric forces, as our working model. This model, together with the analysis and language which emerges from its investigation, serves as a paradigm for analyzing similar behavior in a broad range of situations. I will also use simple phenomenological models which, although they are not direct reductions of any set of equations which describe accurately the microscopic behavior of a real system, are nevertheless useful because one can work out all the mathematical details simply and explicitly and thereby avoid clouding the main ideas with cumbersome calculations.

Original languageEnglish (US)
Title of host publicationPattern Formation in the Physical and Biological Sciences
PublisherCRC Press
Pages201-268
Number of pages68
ISBN (Electronic)9780429961915
ISBN (Print)9780201408447
DOIs
StatePublished - Jan 1 2018

Fingerprint

Cactus
Gravity Waves
Ripple
Shallow Water
Equilibrium State
Ocean
Convection
Bifurcation
Paradigm
Model
Symmetry
Fluid
Configuration
Series
Range of data
Language

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Newell, A. C. (2018). The dynamics and analysis of patterns. In Pattern Formation in the Physical and Biological Sciences (pp. 201-268). CRC Press. https://doi.org/10.1201/9780429493362

The dynamics and analysis of patterns. / Newell, Alan C.

Pattern Formation in the Physical and Biological Sciences. CRC Press, 2018. p. 201-268.

Research output: Chapter in Book/Report/Conference proceedingChapter

Newell, AC 2018, The dynamics and analysis of patterns. in Pattern Formation in the Physical and Biological Sciences. CRC Press, pp. 201-268. https://doi.org/10.1201/9780429493362
Newell AC. The dynamics and analysis of patterns. In Pattern Formation in the Physical and Biological Sciences. CRC Press. 2018. p. 201-268 https://doi.org/10.1201/9780429493362
Newell, Alan C. / The dynamics and analysis of patterns. Pattern Formation in the Physical and Biological Sciences. CRC Press, 2018. pp. 201-268
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