Rigorous derivation of the Landau equation in the weak coupling limit
We examine a family of microscopic models of plasmas, with a parameter [\alpha] comparing the typical distance between collisions to the strength of the grazing collisions. These microscopic models converge in distribution, in the weak coupling limit, to a velocity diffusion described by the linear...
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| Format: | Article |
| Language: | en_US |
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American Institute of Mathematical Sciences
2012
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| Online Access: | http://hdl.handle.net/1721.1/70938 |
| _version_ | 1811077892078043136 |
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| author | Kirkpatrick, Kay |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Kirkpatrick, Kay |
| author_sort | Kirkpatrick, Kay |
| collection | MIT |
| description | We examine a family of microscopic models of plasmas, with a parameter [\alpha] comparing the typical distance between collisions to the strength of the grazing collisions. These microscopic models converge in distribution, in the weak coupling limit, to a velocity diffusion described by the linear Landau equation (also known as the Fokker-Planck equation). The present work extends and unifies previous results that handled the extremes of the parameter [alpha] to the whole range [(0,1 over 2]] ,by showing that clusters of overlapping obstacles are negligible in the limit. Additionally, we study the diffusion coefficient of the Landau equation and show it to be independent of the parameter. |
| first_indexed | 2024-09-23T10:49:56Z |
| format | Article |
| id | mit-1721.1/70938 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:49:56Z |
| publishDate | 2012 |
| publisher | American Institute of Mathematical Sciences |
| record_format | dspace |
| spelling | mit-1721.1/709382022-09-30T23:18:10Z Rigorous derivation of the Landau equation in the weak coupling limit Kirkpatrick, Kay Massachusetts Institute of Technology. Department of Mathematics Kirkpatrick, Kay Kirkpatrick, Kay We examine a family of microscopic models of plasmas, with a parameter [\alpha] comparing the typical distance between collisions to the strength of the grazing collisions. These microscopic models converge in distribution, in the weak coupling limit, to a velocity diffusion described by the linear Landau equation (also known as the Fokker-Planck equation). The present work extends and unifies previous results that handled the extremes of the parameter [alpha] to the whole range [(0,1 over 2]] ,by showing that clusters of overlapping obstacles are negligible in the limit. Additionally, we study the diffusion coefficient of the Landau equation and show it to be independent of the parameter. National Science Foundation (U.S.) (Graduate Research Fellowship) American Association of University Women (AAUW American Dissertation Fellowship) 2012-05-25T14:58:45Z 2012-05-25T14:58:45Z 2009-11 Article http://purl.org/eprint/type/JournalArticle 1534-0392 http://hdl.handle.net/1721.1/70938 Kirkpatrick, Kay. “Rigorous Derivation of the Landau Equation in the Weak Coupling Limit.” Communications on Pure and Applied Analysis 8.6 (2009): 1895–1916. Web.© American Institute of Mathematical Sciences. en_US http://dx.doi.org/10.3934/cpaa.2009.8.1895 Communications on Pure and Applied Analysis Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Institute of Mathematical Sciences AIMS |
| spellingShingle | Kirkpatrick, Kay Rigorous derivation of the Landau equation in the weak coupling limit |
| title | Rigorous derivation of the Landau equation in the weak coupling limit |
| title_full | Rigorous derivation of the Landau equation in the weak coupling limit |
| title_fullStr | Rigorous derivation of the Landau equation in the weak coupling limit |
| title_full_unstemmed | Rigorous derivation of the Landau equation in the weak coupling limit |
| title_short | Rigorous derivation of the Landau equation in the weak coupling limit |
| title_sort | rigorous derivation of the landau equation in the weak coupling limit |
| url | http://hdl.handle.net/1721.1/70938 |
| work_keys_str_mv | AT kirkpatrickkay rigorousderivationofthelandauequationintheweakcouplinglimit |