{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T22:40:07Z","timestamp":1680388807300},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014,3,1]]},"abstract":"<jats:title>Abstract.<\/jats:title>\n               <jats:p>The objective of this paper is the exposition of a recently-developed\nGreen's function Monte Carlo (GFMC) algorithm for the solution of nonlinear\npartial differential equations and its application to the modeling of the\nplasma sheath region around a spherical conducting object, carrying a\npotential and moving at low speeds through a partially ionized medium. The\nplasma sheath is modeled in equilibrium through the GFMC solution of the\nnonlinear Poisson\u2013Boltzmann (NPB) equation. The traditional GFMC-based\napproaches for the solution of nonlinear equations involve the iterative\nsolution of a series of linear problems. Over the last several years, one of\nthe authors of this paper, K. Chatterjee, has been developing a\nphilosophically different approach, where the linearization of the equation\nof interest is not required and hence there is no need for iteration.\nInstead, an approximate expression for the Green's function is obtained\nusing perturbation theory, which is used to formulate the random walk\nequations within the problem sub-domains, where the random-walker makes its\nwalks. On the other hand, as a trade-off, the dimensions of these\nsub-domains have to be restricted by the limitations imposed by perturbation\ntheory. The greatest advantage of this approach is the ease and simplicity\nof parallelization stemming from the lack of the need for iteration, as a\nresult of which the parallelization procedure is identical to the\nparallelization procedure for the GFMC solution of a linear problem.\nHowever, the premise of the algorithm is novel and rigorous mathematical\njustification has to be established in the future. The application areas of\ninterest include the communication blackout problem during a space vehicle's\nre-entry into the atmosphere and electromagnetic propagation through the\natmosphere\/ionosphere in UHF\/GPS applications.<\/jats:p>","DOI":"10.1515\/mcma-2013-0016","type":"journal-article","created":{"date-parts":[[2014,1,14]],"date-time":"2014-01-14T20:36:09Z","timestamp":1389731769000},"page":"53-59","source":"Crossref","is-referenced-by-count":0,"title":["A new Green's function Monte Carlo algorithm for the solution of\nthe three-dimensional nonlinear Poisson\u2013Boltzmann equation:\nApplication to the modeling of plasma sheath layers"],"prefix":"10.1515","volume":"20","author":[{"given":"Kausik","family":"Chatterjee","sequence":"first","affiliation":[{"name":"Strategic and Military Space Division, Space Dynamics Laboratory, North Logan, UT 84341; and Center for Atmospheric and Space Sciences, Utah State University, Logan, UT 84322, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"John R.","family":"Roadcap","sequence":"additional","affiliation":[{"name":"Air Force Research Laboratory, Albuquerque, NM 87117, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Surendra","family":"Singh","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, The University of Tulsa, Tulsa, OK 74104, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2014,1,14]]},"container-title":["mcma"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2013-0016\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2013-0016\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T22:12:08Z","timestamp":1680387128000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2013-0016\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2014,3,1]]},"published-print":{"date-parts":[[2014,3,1]]}},"alternative-id":["10.1515\/mcma-2013-0016"],"URL":"https:\/\/doi.org\/10.1515\/mcma-2013-0016","relation":{},"ISSN":["0929-9629","1569-3961"],"issn-type":[{"value":"0929-9629","type":"print"},{"value":"1569-3961","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1,14]]}}}