{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,6]],"date-time":"2025-10-06T18:05:20Z","timestamp":1759773920063,"version":"3.37.3"},"reference-count":21,"publisher":"Walter de Gruyter GmbH","issue":"2","funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["14-11-00083"],"award-info":[{"award-number":["14-11-00083"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We suggest random walk on semi-infinite cylinders methods for solving interior and exterior diffusion problems\nwith different types of boundary conditions which include mixed Dirichlet, Neumann, and Robin boundary conditions\non different parts of the boundary.\nBased on probabilistic interpretation of the diffusion process,\nstochastic simulation algorithms take into account specific features of each boundary condition to optimally\nadjust the Markov chain distribution on the relevant boundary parts.\nIn contrast to the conventional direct trajectory tracking method, the new method\navoids to simulate the diffusion trajectories.\nInstead, it exploits exact probabilities of different events like the first passage,\nsplitting, and survival probabilities inside the semi-infinite cylinders,\ndepending on the domain and its boundary structure. Applications to diffusion imaging methods like the cathodoluminescence (CL) and\nelectron beam induced current (EBIC) semiconductor analysis techniques performed in scanning\nelectron and transmission microscopes, are discussed.<\/jats:p>","DOI":"10.1515\/mcma-2016-0108","type":"journal-article","created":{"date-parts":[[2016,5,27]],"date-time":"2016-05-27T10:03:04Z","timestamp":1464343384000},"page":"117-131","source":"Crossref","is-referenced-by-count":6,"title":["Random walk on semi-cylinders for diffusion problems with mixed Dirichlet\u2013Robin boundary conditions"],"prefix":"10.1515","volume":"22","author":[{"given":"Karl K.","family":"Sabelfeld","sequence":"first","affiliation":[{"name":"Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Novosibirsk, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2016,5,27]]},"reference":[{"key":"2023040101305240093_j_mcma-2016-0108_ref_000_w2aab2b8c10b1b7b1ab1ab1Aa","doi-asserted-by":"crossref","unstructured":"C. Donolato,\nModeling the effect of dislocations on the minority carrier diffusion length of a semiconductor,\nJ. Appl. Phys. 84 (1998), 5, 2656\u20132664.","DOI":"10.1063\/1.368378"},{"key":"2023040101305240093_j_mcma-2016-0108_ref_001_w2aab2b8c10b1b7b1ab1ab2Aa","unstructured":"E. B. Dynkin,\nMarkov Processes,\nFizmatgiz, Moscow, 1963."},{"key":"2023040101305240093_j_mcma-2016-0108_ref_002_w2aab2b8c10b1b7b1ab1ab3Aa","doi-asserted-by":"crossref","unstructured":"R. Erban and S. J. Chapman,\nReactive boundary conditions for stochastic simulations of reaction\u2013diffusion processes,\nPhys. Biol. 4 (2007), 16\u201328.","DOI":"10.1088\/1478-3975\/4\/1\/003"},{"key":"2023040101305240093_j_mcma-2016-0108_ref_003_w2aab2b8c10b1b7b1ab1ab4Aa","doi-asserted-by":"crossref","unstructured":"S. M. Ermakov, V. V. Nekrutkin and A. S. Sipin,\nRandom Processes for Classical Equations of Mathematical Physics,\nKluwer Academic Publishers, Dordrecht, 1989.","DOI":"10.1007\/978-94-009-2243-3"},{"key":"2023040101305240093_j_mcma-2016-0108_ref_004_w2aab2b8c10b1b7b1ab1ab5Aa","doi-asserted-by":"crossref","unstructured":"A. Friedman,\nStochastic Differential Equations and Applications, Vol. 1\u20132,\nAcademic Press, New York, 1976.","DOI":"10.1016\/B978-0-12-268202-5.50014-2"},{"key":"2023040101305240093_j_mcma-2016-0108_ref_005_w2aab2b8c10b1b7b1ab1ab6Aa","unstructured":"M. Kac,\nProbability and Related Topics in Physical Sciences, Vol. 1,\nAmerican Mathematical Society, Providence, 1959."},{"key":"2023040101305240093_j_mcma-2016-0108_ref_006_w2aab2b8c10b1b7b1ab1ab7Aa","unstructured":"D. Luc,\nNon-Uniform Random Variate Generation,\nSpringer, New York, 1986."},{"key":"2023040101305240093_j_mcma-2016-0108_ref_007_w2aab2b8c10b1b7b1ab1ab8Aa","doi-asserted-by":"crossref","unstructured":"V. A. Markel and J. C. Schotland,\nInverse problem in optical diffusion tomography. II: Role of boundary conditions,\nJ. Optical Soc. Amer. A 19 (2002), 3, 558\u2013566.","DOI":"10.1364\/JOSAA.19.000558"},{"key":"2023040101305240093_j_mcma-2016-0108_ref_008_w2aab2b8c10b1b7b1ab1ab9Aa","doi-asserted-by":"crossref","unstructured":"P. Parish and C. M. Russell,\nOn the use of Monte Carlo modeling in the mathematical analysis of scanning electron microscopy\u2013electron beam induced current data,\nAppl. Phys. Letters 89 (2006), 19, Article ID 192108.","DOI":"10.1063\/1.2385212"},{"key":"2023040101305240093_j_mcma-2016-0108_ref_009_w2aab2b8c10b1b7b1ab1ac10Aa","doi-asserted-by":"crossref","unstructured":"A. D. Polyanin and V. E. Nazaikinskii,\nHandbook of Linear Partial Differential Equations for Engineers and Scientists,\nCRC Press, Boca Raton, 2016.","DOI":"10.1201\/b19056"},{"key":"2023040101305240093_j_mcma-2016-0108_ref_010_w2aab2b8c10b1b7b1ab1ac11Aa","unstructured":"A. P. Prudnikov, J. F. Brychkov and O. I. Marichev,\nIntegrals and Series,\nNauka, Moscow, 1981."},{"key":"2023040101305240093_j_mcma-2016-0108_ref_011_w2aab2b8c10b1b7b1ab1ac12Aa","doi-asserted-by":"crossref","unstructured":"S. Redner,\nA Guide to First-Passage Processes,\nCambridge University Press, Cambridge, 2001.","DOI":"10.1017\/CBO9780511606014"},{"key":"2023040101305240093_j_mcma-2016-0108_ref_012_w2aab2b8c10b1b7b1ab1ac13Aa","doi-asserted-by":"crossref","unstructured":"K. K. Sabelfeld,\nMonte Carlo Methods in Boundary Value Problems,\nSpringer, Berlin, 1991.","DOI":"10.1007\/978-3-642-75977-2"},{"key":"2023040101305240093_j_mcma-2016-0108_ref_013_w2aab2b8c10b1b7b1ab1ac14Aa","doi-asserted-by":"crossref","unstructured":"K. K. Sabelfeld,\nSplitting and survival probabilities in stochastic random walk methods and applications,\nMonte Carlo Methods Appl. 22 (2016), 1, 55\u201372.","DOI":"10.1515\/mcma-2016-0103"},{"key":"2023040101305240093_j_mcma-2016-0108_ref_014_w2aab2b8c10b1b7b1ab1ac15Aa","doi-asserted-by":"crossref","unstructured":"K. K. Sabelfeld,\nStochastic Methods for Boundary Value Problems. Numerics for High-Dimensional PDEs and Applications,\nDe Gruyter, Berlin, 2016.","DOI":"10.1515\/9783110479454"},{"key":"2023040101305240093_j_mcma-2016-0108_ref_015_w2aab2b8c10b1b7b1ab1ac16Aa","doi-asserted-by":"crossref","unstructured":"K. K. Sabelfeld and N. A. Simonov,\nRandom Walks on Boundary for Solving PDEs,\nVSP, Utrecht, 1994.","DOI":"10.1515\/9783110942026"},{"key":"2023040101305240093_j_mcma-2016-0108_ref_016_w2aab2b8c10b1b7b1ab1ac17Aa","unstructured":"N. A. Simonov,\nRandom walk on spheres algorithms for solving mixed and Neumann boundary value problems,\nSib. J. Numer. Math. 10 (2007), 2, 209\u2013220."},{"key":"2023040101305240093_j_mcma-2016-0108_ref_017_w2aab2b8c10b1b7b1ab1ac18Aa","doi-asserted-by":"crossref","unstructured":"N. A. Simonov, M. Mascagni and M. O. Fenley,\nMonte Carlo-based linear Poisson\u2013Boltzmann approach makes accurate salt-dependent solvation free energy predictions possible,\nJ. Chem. Phys. 127 (2007), Article ID 185105.","DOI":"10.1063\/1.2803189"},{"key":"2023040101305240093_j_mcma-2016-0108_ref_018_w2aab2b8c10b1b7b1ab1ac19Aa","doi-asserted-by":"crossref","unstructured":"A. Singer, Z. Schuss, A. Osipov and D. Holcman,\nPartially reflected diffusion,\nSIAM J. Appl. Math. 68 (2007), 3, 844\u2013868.","DOI":"10.1137\/060663258"},{"key":"2023040101305240093_j_mcma-2016-0108_ref_019_w2aab2b8c10b1b7b1ab1ac20Aa","doi-asserted-by":"crossref","unstructured":"A. Sipin,\nMonte Carlo method for partial differential equations,\nTopics in Statistical Simulation (Rimini 2013),\nSpringer Proc. Math. Stat. 114,\nSpringer, New York (2014), 465\u2013473.","DOI":"10.1007\/978-1-4939-2104-1_46"},{"key":"2023040101305240093_j_mcma-2016-0108_ref_020_w2aab2b8c10b1b7b1ab1ac21Aa","doi-asserted-by":"crossref","unstructured":"S. Steisunas,\nOn the sojourn time of the Brownian process in a multidimensional sphere,\nNonlinear Anal. Model. Control 14 (2009), 3, 389\u2013396.","DOI":"10.15388\/NA.2009.14.3.14502"}],"container-title":["Monte Carlo Methods and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2016-0108\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2016-0108\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T20:24:37Z","timestamp":1680380677000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2016-0108\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5,27]]},"references-count":21,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2016,6,1]]},"published-print":{"date-parts":[[2016,6,1]]}},"alternative-id":["10.1515\/mcma-2016-0108"],"URL":"https:\/\/doi.org\/10.1515\/mcma-2016-0108","relation":{},"ISSN":["0929-9629","1569-3961"],"issn-type":[{"type":"print","value":"0929-9629"},{"type":"electronic","value":"1569-3961"}],"subject":[],"published":{"date-parts":[[2016,5,27]]}}}