The Role of Symmetry and Separation in Surface Evolution and Curve Shortening
With few exceptions, known explicit solutions of the curve shortening flow (CSE) of a plane curve, can be constructed by classical Lie point symmetry reductions or by functional separation of variables. One of the functionally separated solutions is the exact curve shortening flow of a closed, conve...
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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2011 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147169 |
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| Цитувати: | The Role of Symmetry and Separation in Surface Evolution and Curve Shortening / P. Broadbridge, P. Vassiliou // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 28 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147169 |
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dspace |
| spelling |
irk-123456789-1471692019-02-14T01:23:27Z The Role of Symmetry and Separation in Surface Evolution and Curve Shortening Broadbridge, P. Vassiliou, P. With few exceptions, known explicit solutions of the curve shortening flow (CSE) of a plane curve, can be constructed by classical Lie point symmetry reductions or by functional separation of variables. One of the functionally separated solutions is the exact curve shortening flow of a closed, convex ''oval''-shaped curve and another is the smoothing of an initial periodic curve that is close to a square wave. The types of anisotropic evaporation coefficient are found for which the evaporation-condensation evolution does or does not have solutions that are analogous to the basic solutions of the CSE, namely the grim reaper travelling wave, the homothetic shrinking closed curve and the homothetically expanding grain boundary groove. Using equivalence classes of anisotropic diffusion equations, it is shown that physical models of evaporation-condensation must have a diffusivity function that decreases as the inverse square of large slope. Some exact separated solutions are constructed for physically consistent anisotropic diffusion equations. 2011 Article The Role of Symmetry and Separation in Surface Evolution and Curve Shortening / P. Broadbridge, P. Vassiliou // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 28 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 35A30; 35K55; 58J70; 74E10 DOI:10.3842/SIGMA.2011.052 http://dspace.nbuv.gov.ua/handle/123456789/147169 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
With few exceptions, known explicit solutions of the curve shortening flow (CSE) of a plane curve, can be constructed by classical Lie point symmetry reductions or by functional separation of variables. One of the functionally separated solutions is the exact curve shortening flow of a closed, convex ''oval''-shaped curve and another is the smoothing of an initial periodic curve that is close to a square wave. The types of anisotropic evaporation coefficient are found for which the evaporation-condensation evolution does or does not have solutions that are analogous to the basic solutions of the CSE, namely the grim reaper travelling wave, the homothetic shrinking closed curve and the homothetically expanding grain boundary groove. Using equivalence classes of anisotropic diffusion equations, it is shown that physical models of evaporation-condensation must have a diffusivity function that decreases as the inverse square of large slope. Some exact separated solutions are constructed for physically consistent anisotropic diffusion equations. |
| format |
Article |
| author |
Broadbridge, P. Vassiliou, P. |
| spellingShingle |
Broadbridge, P. Vassiliou, P. The Role of Symmetry and Separation in Surface Evolution and Curve Shortening Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Broadbridge, P. Vassiliou, P. |
| author_sort |
Broadbridge, P. |
| title |
The Role of Symmetry and Separation in Surface Evolution and Curve Shortening |
| title_short |
The Role of Symmetry and Separation in Surface Evolution and Curve Shortening |
| title_full |
The Role of Symmetry and Separation in Surface Evolution and Curve Shortening |
| title_fullStr |
The Role of Symmetry and Separation in Surface Evolution and Curve Shortening |
| title_full_unstemmed |
The Role of Symmetry and Separation in Surface Evolution and Curve Shortening |
| title_sort |
role of symmetry and separation in surface evolution and curve shortening |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147169 |
| citation_txt |
The Role of Symmetry and Separation in Surface Evolution and Curve Shortening / P. Broadbridge, P. Vassiliou // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 28 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:26:46Z |
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2023-05-20T17:26:46Z |
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