Relation between the connected diagram and smoothing methods for rough surface scattering
In previous work by the author on connected diagram expansion methods for the problem of scattering from a random rough surface a stochastic Lippmann–Schwinger integral equation in Fourier transform space for the scattered part of the Green’s function was derived. Averaging techniques using homogene...
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Veröffentlicht in: | Journal of mathematical physics 1986-01, Vol.27 (1), p.377-379 |
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description | In previous work by the author on connected diagram expansion methods for the problem of scattering from a random rough surface a stochastic Lippmann–Schwinger integral equation in Fourier transform space for the scattered part of the Green’s function was derived. Averaging techniques using homogeneous statistics and a statistical cluster decomposition on the surface interaction function yielded a connected diagram expansion for the coherent and incoherent Green’s functions. Here it is demonstrated that the smoothing method applied to this stochastic integral equation yields a result that agrees with the connected diagram expansion only to second order in the surface interaction. For third‐ and higher‐order interactions, the smoothing method does not yield connected terms. |
doi_str_mv | 10.1063/1.527343 |
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Averaging techniques using homogeneous statistics and a statistical cluster decomposition on the surface interaction function yielded a connected diagram expansion for the coherent and incoherent Green’s functions. Here it is demonstrated that the smoothing method applied to this stochastic integral equation yields a result that agrees with the connected diagram expansion only to second order in the surface interaction. For third‐ and higher‐order interactions, the smoothing method does not yield connected terms.</description><identifier>ISSN: 0022-2488</identifier><identifier>EISSN: 1089-7658</identifier><identifier>DOI: 10.1063/1.527343</identifier><identifier>CODEN: JMAPAQ</identifier><language>eng</language><publisher>Melville, NY: American Institute of Physics</publisher><subject>Exact sciences and technology ; Function theory, analysis ; Mathematical methods in physics ; Physics</subject><ispartof>Journal of mathematical physics, 1986-01, Vol.27 (1), p.377-379</ispartof><rights>American Institute of Physics</rights><rights>1986 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c388t-680574f06f8473d8513f45d6259dddf6d00028e8cf0ba9676b4119e0a9b94b863</citedby><cites>FETCH-LOGICAL-c388t-680574f06f8473d8513f45d6259dddf6d00028e8cf0ba9676b4119e0a9b94b863</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://pubs.aip.org/jmp/article-lookup/doi/10.1063/1.527343$$EHTML$$P50$$Gscitation$$H</linktohtml><link.rule.ids>314,780,784,1559,4024,27923,27924,27925,76390</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=8777502$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>DeSanto, John A.</creatorcontrib><title>Relation between the connected diagram and smoothing methods for rough surface scattering</title><title>Journal of mathematical physics</title><description>In previous work by the author on connected diagram expansion methods for the problem of scattering from a random rough surface a stochastic Lippmann–Schwinger integral equation in Fourier transform space for the scattered part of the Green’s function was derived. Averaging techniques using homogeneous statistics and a statistical cluster decomposition on the surface interaction function yielded a connected diagram expansion for the coherent and incoherent Green’s functions. Here it is demonstrated that the smoothing method applied to this stochastic integral equation yields a result that agrees with the connected diagram expansion only to second order in the surface interaction. 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Averaging techniques using homogeneous statistics and a statistical cluster decomposition on the surface interaction function yielded a connected diagram expansion for the coherent and incoherent Green’s functions. Here it is demonstrated that the smoothing method applied to this stochastic integral equation yields a result that agrees with the connected diagram expansion only to second order in the surface interaction. For third‐ and higher‐order interactions, the smoothing method does not yield connected terms.</abstract><cop>Melville, NY</cop><pub>American Institute of Physics</pub><doi>10.1063/1.527343</doi><tpages>3</tpages></addata></record> |
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subjects | Exact sciences and technology Function theory, analysis Mathematical methods in physics Physics |
title | Relation between the connected diagram and smoothing methods for rough surface scattering |
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