Global description of patterns far from onset: A case study

N. Ercolani; R. Indik; A. C. Newell; T. Passot

doi:10.1016/S0167-2789(03)00217-3

Global description of patterns far from onset: A case study

N. Ercolani, R. Indik, A. C. Newell, T. Passot

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

The Cross-Newell phase diffusion equation τ(k)Θ_T = - ∇ · k^→B(k), k^→ = ∇Θ, |k^→| = k, and its regularization describe patterns and defects far from onset in large aspect ratio systems with translational and rotational symmetry. In this paper we show how director field solutions of this equation can be used to describe features of global patterns. The ideas are illustrated in the context of a non-trivial case study of high Prandtl number convection in a large aspect ratio, shallow, elliptical container with heated sidewalls, for which we also have the results of simulation and experiment.

Original language	English (US)
Pages (from-to)	127-140
Number of pages	14
Journal	Physica D: Nonlinear Phenomena
Volume	184
Issue number	1-4
DOIs	https://doi.org/10.1016/S0167-2789(03)00217-3
State	Published - Oct 1 2003

Keywords

Convection
Defects
Patterns

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/S0167-2789(03)00217-3

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title = "Global description of patterns far from onset: A case study",

abstract = "The Cross-Newell phase diffusion equation τ(k)ΘT = - ∇ · k→B(k), k→ = ∇Θ, |k→| = k, and its regularization describe patterns and defects far from onset in large aspect ratio systems with translational and rotational symmetry. In this paper we show how director field solutions of this equation can be used to describe features of global patterns. The ideas are illustrated in the context of a non-trivial case study of high Prandtl number convection in a large aspect ratio, shallow, elliptical container with heated sidewalls, for which we also have the results of simulation and experiment.",

keywords = "Convection, Defects, Patterns",

author = "N. Ercolani and R. Indik and Newell, {A. C.} and T. Passot",

note = "Funding Information: The authors wish to thank Joceline Lega for many helpful discussions and in particular for generating Fig. 3 . The authors also wish to thank Guenter Ahlers and Mark Paul for helpful discussion and for generosity in sharing their results. NME would like to acknowledge support from NSF grant DMS-0073087 and ACN would like to acknowledge support from NSF grant DMS-0072803.",

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doi = "10.1016/S0167-2789(03)00217-3",

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T1 - Global description of patterns far from onset

T2 - A case study

AU - Ercolani, N.

AU - Indik, R.

AU - Newell, A. C.

AU - Passot, T.

N1 - Funding Information: The authors wish to thank Joceline Lega for many helpful discussions and in particular for generating Fig. 3 . The authors also wish to thank Guenter Ahlers and Mark Paul for helpful discussion and for generosity in sharing their results. NME would like to acknowledge support from NSF grant DMS-0073087 and ACN would like to acknowledge support from NSF grant DMS-0072803.

PY - 2003/10/1

Y1 - 2003/10/1

N2 - The Cross-Newell phase diffusion equation τ(k)ΘT = - ∇ · k→B(k), k→ = ∇Θ, |k→| = k, and its regularization describe patterns and defects far from onset in large aspect ratio systems with translational and rotational symmetry. In this paper we show how director field solutions of this equation can be used to describe features of global patterns. The ideas are illustrated in the context of a non-trivial case study of high Prandtl number convection in a large aspect ratio, shallow, elliptical container with heated sidewalls, for which we also have the results of simulation and experiment.

AB - The Cross-Newell phase diffusion equation τ(k)ΘT = - ∇ · k→B(k), k→ = ∇Θ, |k→| = k, and its regularization describe patterns and defects far from onset in large aspect ratio systems with translational and rotational symmetry. In this paper we show how director field solutions of this equation can be used to describe features of global patterns. The ideas are illustrated in the context of a non-trivial case study of high Prandtl number convection in a large aspect ratio, shallow, elliptical container with heated sidewalls, for which we also have the results of simulation and experiment.

KW - Convection

KW - Defects

KW - Patterns

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JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

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IS - 1-4

ER -

Global description of patterns far from onset: A case study

Abstract

Keywords

ASJC Scopus subject areas

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