Exact solution for the Poisson field in a semi-infinite strip
The Poisson equation is associated with many physical processes. Yet exact analytic solutions for the two-dimensional Poisson field are scarce. Here we derive an analytic solution for the Poisson equation with constant forcing in a semi-infinite strip. We provide a method that can be used to solve t...
| Main Authors: | , |
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| Format: | Article |
| Language: | en_US |
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Royal Society
2018
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| Online Access: | http://hdl.handle.net/1721.1/119793 https://orcid.org/0000-0002-7997-0119 https://orcid.org/0000-0003-4006-7771 |
| _version_ | 1826204834527707136 |
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| author | Cohen, Yosef Rothman, Daniel H. |
| author2 | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences |
| author_facet | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Cohen, Yosef Rothman, Daniel H. |
| author_sort | Cohen, Yosef |
| collection | MIT |
| description | The Poisson equation is associated with many physical processes. Yet exact analytic solutions for the two-dimensional Poisson field are scarce. Here we derive an analytic solution for the Poisson equation with constant forcing in a semi-infinite strip. We provide a method that can be used to solve the field in other intricate geometries. We show that the Poisson flux reveals an inverse square-root singularity at a tip of a slit, and identify a characteristic length scale in which a small perturbation, in a form of a new slit, is screened by the field. We suggest that this length scale expresses itself as a characteristic spacing between tips in real Poisson networks that grow in response to fluxes at tips. |
| first_indexed | 2024-09-23T13:02:08Z |
| format | Article |
| id | mit-1721.1/119793 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:02:08Z |
| publishDate | 2018 |
| publisher | Royal Society |
| record_format | dspace |
| spelling | mit-1721.1/1197932024-05-15T06:57:33Z Exact solution for the Poisson field in a semi-infinite strip Cohen, Yosef Rothman, Daniel H. Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Rothman Daniel Cohen, Yosef Rothman, Daniel H The Poisson equation is associated with many physical processes. Yet exact analytic solutions for the two-dimensional Poisson field are scarce. Here we derive an analytic solution for the Poisson equation with constant forcing in a semi-infinite strip. We provide a method that can be used to solve the field in other intricate geometries. We show that the Poisson flux reveals an inverse square-root singularity at a tip of a slit, and identify a characteristic length scale in which a small perturbation, in a form of a new slit, is screened by the field. We suggest that this length scale expresses itself as a characteristic spacing between tips in real Poisson networks that grow in response to fluxes at tips. 2018-12-20T14:55:37Z 2018-12-20T14:55:37Z 2017-04 Article http://purl.org/eprint/type/JournalArticle 1364-5021 1471-2946 http://hdl.handle.net/1721.1/119793 Cohen, Yossi, and Daniel H. Rothman. “Exact Solution for the Poisson Field in a Semi-Infinite Strip.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 473, no. 2200 (April 2017): 20160908. https://orcid.org/0000-0002-7997-0119 https://orcid.org/0000-0003-4006-7771 en_US http://dx.doi.org/10.1098/rspa.2016.0908 Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Royal Society Prof. Rothman via Chris Sherratt |
| spellingShingle | Cohen, Yosef Rothman, Daniel H. Exact solution for the Poisson field in a semi-infinite strip |
| title | Exact solution for the Poisson field in a semi-infinite strip |
| title_full | Exact solution for the Poisson field in a semi-infinite strip |
| title_fullStr | Exact solution for the Poisson field in a semi-infinite strip |
| title_full_unstemmed | Exact solution for the Poisson field in a semi-infinite strip |
| title_short | Exact solution for the Poisson field in a semi-infinite strip |
| title_sort | exact solution for the poisson field in a semi infinite strip |
| url | http://hdl.handle.net/1721.1/119793 https://orcid.org/0000-0002-7997-0119 https://orcid.org/0000-0003-4006-7771 |
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