A variational theory for point defects in patterns

N. M. Ercolani; S. C. Venkataramani

doi:10.1007/s00332-008-9035-9

A variational theory for point defects in patterns

N. M. Ercolani, S. C. Venkataramani

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

18 Scopus citations

Abstract

We derive a rigorous scaling law for minimizers in a natural version of the regularized Cross-Newell model for pattern formation far from threshold. These energy-minimizing solutions support defects having the same character as what is seen in experimental studies of the corresponding physical systems and in numerical simulations of the microscopic equations that describe these systems.

Original language	English (US)
Pages (from-to)	267-300
Number of pages	34
Journal	Journal of Nonlinear Science
Volume	19
Issue number	3
DOIs	https://doi.org/10.1007/s00332-008-9035-9
State	Published - Jun 2009

Keywords

Calculus of variations
Defects
Patterns

ASJC Scopus subject areas

Modeling and Simulation
General Engineering
Applied Mathematics

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10.1007/s00332-008-9035-9

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abstract = "We derive a rigorous scaling law for minimizers in a natural version of the regularized Cross-Newell model for pattern formation far from threshold. These energy-minimizing solutions support defects having the same character as what is seen in experimental studies of the corresponding physical systems and in numerical simulations of the microscopic equations that describe these systems.",

keywords = "Calculus of variations, Defects, Patterns",

author = "Ercolani, {N. M.} and Venkataramani, {S. C.}",

note = "Funding Information: Acknowledgements We are grateful to the editor and referees and for their careful reading of the initial draft and their many constructive suggestions. N.M. Ercolani was supported in part by NSF grant DMS-0073087; S.C. Venkataramani was supported in part by an NSF CAREER Award DMS-0135078.",

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doi = "10.1007/s00332-008-9035-9",

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AU - Ercolani, N. M.

AU - Venkataramani, S. C.

N1 - Funding Information: Acknowledgements We are grateful to the editor and referees and for their careful reading of the initial draft and their many constructive suggestions. N.M. Ercolani was supported in part by NSF grant DMS-0073087; S.C. Venkataramani was supported in part by an NSF CAREER Award DMS-0135078.

PY - 2009/6

Y1 - 2009/6

N2 - We derive a rigorous scaling law for minimizers in a natural version of the regularized Cross-Newell model for pattern formation far from threshold. These energy-minimizing solutions support defects having the same character as what is seen in experimental studies of the corresponding physical systems and in numerical simulations of the microscopic equations that describe these systems.

AB - We derive a rigorous scaling law for minimizers in a natural version of the regularized Cross-Newell model for pattern formation far from threshold. These energy-minimizing solutions support defects having the same character as what is seen in experimental studies of the corresponding physical systems and in numerical simulations of the microscopic equations that describe these systems.

KW - Calculus of variations

KW - Defects

KW - Patterns

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JF - Journal of Nonlinear Science

IS - 3

ER -

A variational theory for point defects in patterns

Abstract

Keywords

ASJC Scopus subject areas

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