{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:51:52Z","timestamp":1777449112972,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"3-4","license":[{"start":{"date-parts":[[2014,4,1]],"date-time":"2014-04-01T00:00:00Z","timestamp":1396310400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2014,4]]},"abstract":"<jats:p>In this paper we study the magneto-resistance, i.e. the second-order term of the resistivity perturbed by a low magnetic field, of a three-dimensional composite material. Extending the two-dimensional periodic framework of [Mathematical Models and Methods in Applied Sciences 20(7) (2010), 1161\u20131177], it is proved through a H-convergence approach that the dissipation energy induced by the effective magneto-resistance is greater or equal to the average of the dissipation energy induced by the magneto-resistance in each phase of the composite. This inequality validates for a composite material the Kohler law which is known for a homogeneous conductor. The case of equality is shown to be very sensitive to the magnetic field orientation. We illustrate the result with layered and columnar periodic structures.<\/jats:p>","DOI":"10.3233\/asy-131192","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:31:33Z","timestamp":1575055893000},"page":"165-197","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Magneto-resistance in three-dimensional composites"],"prefix":"10.1177","volume":"86","author":[{"given":"Marc","family":"Briane","sequence":"first","affiliation":[{"name":"Institut de Recherche Math\u00e9matique de Rennes, INSA de Rennes, Rennes, France. E-mail: mbriane@insa-rennes.fr"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Laurent","family":"Pater","sequence":"additional","affiliation":[{"name":"Institut de Recherche Math\u00e9matique de Rennes, Universit\u00e9 de Rennes 1, Rennes, France. E-mail: laurent.pater@ens-cachan.org"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2014,4,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-131192","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-131192","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:40:04Z","timestamp":1777380004000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-131192"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,4]]},"references-count":0,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2014,4]]}},"alternative-id":["10.3233\/ASY-131192"],"URL":"https:\/\/doi.org\/10.3233\/asy-131192","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,4]]}}}