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In this work, it is shown that the idea of comparing models and controlling model error can be used to develop a general approach for multiscale modeling, a subject of growing importance in computational science. A posteriori estimates of modeling error in so\u2010called quantities of interest are derived and a class of adaptive modeling algorithms is presented. Several applications of the theory and methodology are presented. These include preliminary work on random multiphase composite materials, molecular statics simulations with applications to problems in nanoindentation, and analysis of molecular dynamics models using various techniques for scale bridging.<\/jats:p>","DOI":"10.1137\/050632488","type":"journal-article","created":{"date-parts":[[2007,1,10]],"date-time":"2007-01-10T09:51:43Z","timestamp":1168422703000},"page":"2359-2389","source":"Crossref","is-referenced-by-count":95,"title":["MultiScale Modeling of Physical Phenomena: Adaptive Control of Models"],"prefix":"10.1137","volume":"28","author":[{"given":"J.","family":"Tinsley Oden","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Serge","family":"Prudhomme","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Albert","family":"Romkes","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Paul T.","family":"Bauman","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,12,26]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"M. 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