dorsal/arxiv
View SchemaDomain Structures in Fourth-Order Phase and Ginzburg-Landau Equations
| Authors | David Raitt, Hermann Riecke |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9402003 |
| URL | https://arxiv.org/abs/patt-sol/9402003 |
| DOI | 10.1016/0167-2789(94)00218-F |
| Journal | Physica D 82 1995 79-94 |
Abstract
In pattern-forming systems, competition between patterns with different wave numbers can lead to domain structures, which consist of regions with differing wave numbers separated by domain walls. For domain structures well above threshold we employ the appropriate phase equation and obtain detailed qualitative agreement with recent experiments. Close to threshold a fourth-order Ginzburg-Landau equation is used which describes a steady bifurcation in systems with two competing critical wave numbers. The existence and stability regime of domain structures is found to be very intricate due to interactions with other modes. In contrast to the phase equation the Ginzburg-Landau equation allows a spatially oscillatory interaction of the domain walls. Thus, close to threshold domain structures need not undergo the coarsening dynamics found in the phase equation far above threshold, and can be stable even without phase conservation. We study their regime of stability as a function of their (quantized) length. Domain structures are related to zig-zags in two-dimensional systems. The latter are therefore expected to be stable only when quenched far enough beyond the zig-zag instability.
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"abstract": "In pattern-forming systems, competition between patterns with different wave\nnumbers can lead to domain structures, which consist of regions with differing\nwave numbers separated by domain walls. For domain structures well above\nthreshold we employ the appropriate phase equation and obtain detailed\nqualitative agreement with recent experiments. Close to threshold a\nfourth-order Ginzburg-Landau equation is used which describes a steady\nbifurcation in systems with two competing critical wave numbers. The existence\nand stability regime of domain structures is found to be very intricate due to\ninteractions with other modes.\n In contrast to the phase equation the Ginzburg-Landau equation allows a\nspatially oscillatory interaction of the domain walls. Thus, close to threshold\ndomain structures need not undergo the coarsening dynamics found in the phase\nequation far above threshold, and can be stable even without phase\nconservation. We study their regime of stability as a function of their\n(quantized) length. Domain structures are related to zig-zags in\ntwo-dimensional systems. The latter are therefore expected to be stable only\nwhen quenched far enough beyond the zig-zag instability.",
"arxiv_id": "patt-sol/9402003",
"authors": [
"David Raitt",
"Hermann Riecke"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"doi": "10.1016/0167-2789(94)00218-F",
"journal_ref": "Physica D 82 1995 79-94",
"title": "Domain Structures in Fourth-Order Phase and Ginzburg-Landau Equations",
"url": "https://arxiv.org/abs/patt-sol/9402003"
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