A New Measure of Coarseness for Solutions to Cahn--Hilliard Equations
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915744402374656 |
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| author | Howard, Peter Larios, Adam Lin, Quyuan |
| author_facet | Howard, Peter Larios, Adam Lin, Quyuan |
| contents | We introduce a new measure of coarseness for characterizing phase separation processes such as those described by Cahn--Hilliard equations. An advantage of our measure is that it remains consistent throughout the evolution, including for solutions with no periodic structure. We use our measure to compare two previous models of coarsening dynamics with numerically generated dynamics, providing the first direct check that we are aware of for the efficacy of these methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15134 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A New Measure of Coarseness for Solutions to Cahn--Hilliard Equations Howard, Peter Larios, Adam Lin, Quyuan Analysis of PDEs 35B99 (primary), 35Q99 (secondary) We introduce a new measure of coarseness for characterizing phase separation processes such as those described by Cahn--Hilliard equations. An advantage of our measure is that it remains consistent throughout the evolution, including for solutions with no periodic structure. We use our measure to compare two previous models of coarsening dynamics with numerically generated dynamics, providing the first direct check that we are aware of for the efficacy of these methods. |
| title | A New Measure of Coarseness for Solutions to Cahn--Hilliard Equations |
| topic | Analysis of PDEs 35B99 (primary), 35Q99 (secondary) |
| url | https://arxiv.org/abs/2601.15134 |