dorsal/arxiv
View SchemaThe Swift-Hohenberg Equation Requires Non-Local Modifications to Model Spatial Pattern Evolution of Physical Problems
| Authors | A. J. Roberts |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9412002 |
| URL | https://arxiv.org/abs/patt-sol/9412002 |
Abstract
I argue that ``good'' mathematical models of spatio-temporal dynamics in two-dimensions require non-local operators in the nonlinear terms. Consequently, the often used Swift-Hohenberg equation requires modification as it is purely local. My aim here is to provoke more critical examination of the rationale for using the Swift-Hohenberg equations as a reliable model of the spatial pattern evolution in specific physical systems.
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"abstract": "I argue that ``good\u0027\u0027 mathematical models of spatio-temporal dynamics in\ntwo-dimensions require non-local operators in the nonlinear terms.\nConsequently, the often used Swift-Hohenberg equation requires modification as\nit is purely local. My aim here is to provoke more critical examination of the\nrationale for using the Swift-Hohenberg equations as a reliable model of the\nspatial pattern evolution in specific physical systems.",
"arxiv_id": "patt-sol/9412002",
"authors": [
"A. J. Roberts"
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"title": "The Swift-Hohenberg Equation Requires Non-Local Modifications to Model Spatial Pattern Evolution of Physical Problems",
"url": "https://arxiv.org/abs/patt-sol/9412002"
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