Γ-convergence of a shearlet-based Ginzburg–Landau energy
We introduce two shearlet-based Ginzburg–Landau energies, based on the continuous and the discrete shearlet transform. The energies result from replacing the elastic energy term of a classical Ginzburg–Landau energy by the weighted -norm of a shearlet transform. The asymptotic behaviour of sequences...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Elsevier
2020
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| _version_ | 1797111920839360512 |
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| author | Petersen, P Süli, E |
| author_facet | Petersen, P Süli, E |
| author_sort | Petersen, P |
| collection | OXFORD |
| description | We introduce two shearlet-based Ginzburg–Landau energies, based on the continuous and the discrete shearlet transform. The energies result from replacing the elastic energy term of a classical Ginzburg–Landau energy by the weighted -norm of a shearlet transform. The asymptotic behaviour of sequences of these energies is analysed within the framework of Γ-convergence and the limit energy is identified. We show that the limit energy of a characteristic function is an anisotropic surface integral over the interfaces of that function. We demonstrate that the anisotropy of the limit energy can be controlled by weighting the underlying shearlet transforms according to their directional parameter. |
| first_indexed | 2024-03-07T08:15:36Z |
| format | Journal article |
| id | oxford-uuid:63ddfa6c-63e1-4c4b-875c-6acb277d6c27 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:15:36Z |
| publishDate | 2020 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:63ddfa6c-63e1-4c4b-875c-6acb277d6c272024-01-04T12:48:18ZΓ-convergence of a shearlet-based Ginzburg–Landau energyJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:63ddfa6c-63e1-4c4b-875c-6acb277d6c27EnglishSymplectic Elements at OxfordElsevier2020Petersen, PSüli, EWe introduce two shearlet-based Ginzburg–Landau energies, based on the continuous and the discrete shearlet transform. The energies result from replacing the elastic energy term of a classical Ginzburg–Landau energy by the weighted -norm of a shearlet transform. The asymptotic behaviour of sequences of these energies is analysed within the framework of Γ-convergence and the limit energy is identified. We show that the limit energy of a characteristic function is an anisotropic surface integral over the interfaces of that function. We demonstrate that the anisotropy of the limit energy can be controlled by weighting the underlying shearlet transforms according to their directional parameter. |
| spellingShingle | Petersen, P Süli, E Γ-convergence of a shearlet-based Ginzburg–Landau energy |
| title | Γ-convergence of a shearlet-based Ginzburg–Landau energy |
| title_full | Γ-convergence of a shearlet-based Ginzburg–Landau energy |
| title_fullStr | Γ-convergence of a shearlet-based Ginzburg–Landau energy |
| title_full_unstemmed | Γ-convergence of a shearlet-based Ginzburg–Landau energy |
| title_short | Γ-convergence of a shearlet-based Ginzburg–Landau energy |
| title_sort | γ convergence of a shearlet based ginzburg landau energy |
| work_keys_str_mv | AT petersenp gconvergenceofashearletbasedginzburglandauenergy AT sulie gconvergenceofashearletbasedginzburglandauenergy |