EXPONENTIAL ASYMPTOTICS FOR THIN FILM RUPTURE
The formation of singularities in models of many physical systems can be described using self-similar solutions. One particular example is the finite-time rupture of a thin film of viscous fluid which coats a solid substrate. Previous studies have suggested the existence of a discrete, countably inf...
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| Format: | Journal article |
| Language: | English |
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2013
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| _version_ | 1797063236537810944 |
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| author | Chapman, S Trinh, P Witelski, T |
| author_facet | Chapman, S Trinh, P Witelski, T |
| author_sort | Chapman, S |
| collection | OXFORD |
| description | The formation of singularities in models of many physical systems can be described using self-similar solutions. One particular example is the finite-time rupture of a thin film of viscous fluid which coats a solid substrate. Previous studies have suggested the existence of a discrete, countably infinite number of distinct solutions of the nonlinear differential equation which describes the self-similar behavior. However, no analytical mechanism for determining these solutions was identified. In this paper, we use techniques in exponential asymptotics to construct the analytical selection condition for the infinite sequence of similarity solutions, confirming the conjectures of earlier numerical studies. © 2013 Society for Industrial and Applied Mathematics. |
| first_indexed | 2024-03-06T20:56:56Z |
| format | Journal article |
| id | oxford-uuid:3994b669-c040-4b06-9543-0d25e2ce7088 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:56:56Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | oxford-uuid:3994b669-c040-4b06-9543-0d25e2ce70882022-03-26T13:56:24ZEXPONENTIAL ASYMPTOTICS FOR THIN FILM RUPTUREJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3994b669-c040-4b06-9543-0d25e2ce7088EnglishSymplectic Elements at Oxford2013Chapman, STrinh, PWitelski, TThe formation of singularities in models of many physical systems can be described using self-similar solutions. One particular example is the finite-time rupture of a thin film of viscous fluid which coats a solid substrate. Previous studies have suggested the existence of a discrete, countably infinite number of distinct solutions of the nonlinear differential equation which describes the self-similar behavior. However, no analytical mechanism for determining these solutions was identified. In this paper, we use techniques in exponential asymptotics to construct the analytical selection condition for the infinite sequence of similarity solutions, confirming the conjectures of earlier numerical studies. © 2013 Society for Industrial and Applied Mathematics. |
| spellingShingle | Chapman, S Trinh, P Witelski, T EXPONENTIAL ASYMPTOTICS FOR THIN FILM RUPTURE |
| title | EXPONENTIAL ASYMPTOTICS FOR THIN FILM RUPTURE |
| title_full | EXPONENTIAL ASYMPTOTICS FOR THIN FILM RUPTURE |
| title_fullStr | EXPONENTIAL ASYMPTOTICS FOR THIN FILM RUPTURE |
| title_full_unstemmed | EXPONENTIAL ASYMPTOTICS FOR THIN FILM RUPTURE |
| title_short | EXPONENTIAL ASYMPTOTICS FOR THIN FILM RUPTURE |
| title_sort | exponential asymptotics for thin film rupture |
| work_keys_str_mv | AT chapmans exponentialasymptoticsforthinfilmrupture AT trinhp exponentialasymptoticsforthinfilmrupture AT witelskit exponentialasymptoticsforthinfilmrupture |