{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:31:13Z","timestamp":1787229073545,"version":"build-2736575974"},"reference-count":17,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Multiscale Model. Simul."],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>This paper deals with the homogenization of the Hall effect in three-dimensional composites. We prove that the homogenized Hall coefficients are bounded from above by means of prescribed bounds on the local conductivity and the local Hall coefficient. Then, three microstructures of different nature are presented in order to show that arbitrarily large effective Hall coefficients may be obtained in dimension three if the previous prescribed bounds do not hold.<\/jats:p>","DOI":"10.1137\/08073189x","type":"journal-article","created":{"date-parts":[[2009,3,25]],"date-time":"2009-03-25T18:04:14Z","timestamp":1238004254000},"page":"1405-1427","source":"Crossref","is-referenced-by-count":12,"title":["Giant Hall Effect in Composites"],"prefix":"10.1137","volume":"7","author":[{"given":"Marc","family":"Briane","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Graeme W.","family":"Milton","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,3,25]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.61.2472"},{"key":"R2","unstructured":"A. Bensoussan, J.L. Lions, and G. Papanicolaou,\n                      Asymptotic Analysis for Periodic Structures\n                      , North-Holland, Amsterdam, 1978."},{"key":"R3","unstructured":"D.J. Bergman,\n                      Self duality and the low field Hall effect in 2D and 3D metal-insulator composites\n                      , in Percolation Structures and Processes, G. Deutscher, R. Zallen, and J. Adler, eds., Adam Hilger, Bristol, UK, 1983, pp. 297\u2013321."},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/j.physb.2006.12.032"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.50.1512"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4371(97)00095-2"},{"key":"R7","first-page":"357","volume":"4","author":"Briane M.","year":"1994","journal-title":"Adv. Math. Sci. Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/1343-4373","issn-type":"print"},{"key":"R8","unstructured":"M. Briane and G.W. Milton,\n                      Homogenization of the three-dimensional Hall effect and change of sign of the Hall coefficient\n                      , Arch. Ration. Mech. Anal., to appear; published online doi:10.1007\/s00205-008-0200-y, available at http:\/\/www.springerlink.com\/content\/a10vt32208755861."},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2007.07.044"},{"key":"R10","unstructured":"L. Landau and E. Lifshitz,\n                      \u00c9lectrodynamique des Milieux Continus\n                      , \u00c9ditions Mir, Moscow, 1969."},{"key":"R11","doi-asserted-by":"crossref","unstructured":"G. W. Milton,\n                      Modelling the properties of composites by laminates\n                      , in Homogenization and Effective Moduli of Materials and Media, IMA Vol. Math Appl., 1, Springer-Verlag, New York, 1986, pp. 150.","DOI":"10.1007\/978-1-4613-8646-9_7"},{"key":"R12","doi-asserted-by":"crossref","unstructured":"F. Murat and L. Tartar,\n                      H-convergence\n                      , in Topics in the Mathematical Modelling of Composite Materials, Progr. Nonlinear Differential Equations Appl., Birk\u00e4user, Boston, L. Cherkaev and R.V. Kohn eds., 1998, pp. 21\u201343.","DOI":"10.1007\/978-1-4612-2032-9_3"},{"key":"R13","unstructured":"M. Ali Omar,\n                      Elementary Solid State Physics\n                      , World Student Series Edition, Addison-Wesley, Reading, MA, 1975."},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.36.7289"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1088\/0022-3719\/10\/3\/011"},{"key":"R16","unstructured":"L. Tartar,\n                      Compensated compactness and applications to partial differential equations\n                      , in Nonlinear Analysis and Mechanics, Res. Notes Math. 39, R.J. Knops, ed., Pitman, Boston, 1979, pp. 136\u2013212."},{"key":"R17","doi-asserted-by":"crossref","unstructured":"L. Tartar,\n                      An introduction to the homogenization method in optimal design\n                      , in Optimal Shape Design, Lecture Notes in Math.  1740, Springer-Verlag, New York, 2000, pp. 47\u2013156.","DOI":"10.1007\/BFb0106742"}],"container-title":["Multiscale Modeling &amp; Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/08073189X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:18:29Z","timestamp":1787228309000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/08073189X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":17,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1137\/08073189X"],"URL":"https:\/\/doi.org\/10.1137\/08073189x","relation":{},"ISSN":["1540-3459","1540-3467"],"issn-type":[{"value":"1540-3459","type":"print"},{"value":"1540-3467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}