Integrability-preserving regularizations of Laplacian Growth
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929339209089024 |
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| author | Teodorescu, Razvan |
| author_facet | Teodorescu, Razvan |
| contents | The Laplacian Growth (LG) model is known as a universality class of scale-free aggregation models in two dimensions, characterized by classical integrability and featuring finite-time boundary singularity formation. A discrete counterpart, Diffusion-Limited Aggregation (or DLA), has a similar local growth law, but significantly different global behavior. For both LG and DLA, a proper description for the scaling properties of long-time solutions is not available yet. In this note, we outline a possible approach towards finding the correct theory yielding a regularized LG and its relation to DLA. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06167 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Integrability-preserving regularizations of Laplacian Growth Teodorescu, Razvan Mathematical Physics Dynamical Systems Statistics Theory Primary: 30D05, Secondary: 30E10, 30E25 The Laplacian Growth (LG) model is known as a universality class of scale-free aggregation models in two dimensions, characterized by classical integrability and featuring finite-time boundary singularity formation. A discrete counterpart, Diffusion-Limited Aggregation (or DLA), has a similar local growth law, but significantly different global behavior. For both LG and DLA, a proper description for the scaling properties of long-time solutions is not available yet. In this note, we outline a possible approach towards finding the correct theory yielding a regularized LG and its relation to DLA. |
| title | Integrability-preserving regularizations of Laplacian Growth |
| topic | Mathematical Physics Dynamical Systems Statistics Theory Primary: 30D05, Secondary: 30E10, 30E25 |
| url | https://arxiv.org/abs/2405.06167 |