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Emerging Frontiers in Nonlinear Science pp 279–303Cite as

Dissipative Systems

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Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 32))

Abstract

This chapter focuses on pattern formation, both extended and localized, in driven dissipative systems. The origin of localized states and their organization into a snakes-and-ladders structure is explained and the results illustrated with several examples drawn from the physical sciences. The corresponding results for systems with a conserved quantity are described, focusing on crystallization from a supercooled melt via a propagating crystallization front. Unsolved questions are highlighted throughout.

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Acknowledgements

This chapter is dedicated to the memory of Patrick Woods whose work [27] started it all; its preparation was supported in part by NSF grant DMS-1908891.

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Authors and Affiliations

  1. Department of Physics, University of California at Berkeley, Berkeley, CA, 94720, USA

    Edgar Knobloch

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  1. Edgar Knobloch
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Correspondence to Edgar Knobloch .

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Editors and Affiliations

  1. Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, USA

    Panayotis G. Kevrekidis

  2. Grupo de Fisica No Lineal, Departamento de Fisica Aplicada I, Escuela Politécnica Superior, Universidad de Sevilla, Seville, Spain

    Jesús Cuevas-Maraver

  3. Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA

    Avadh Saxena

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Knobloch, E. (2020). Dissipative Systems. In: Kevrekidis, P., Cuevas-Maraver, J., Saxena, A. (eds) Emerging Frontiers in Nonlinear Science. Nonlinear Systems and Complexity, vol 32. Springer, Cham. https://doi.org/10.1007/978-3-030-44992-6_12

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