{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:38:00Z","timestamp":1787337480988,"version":"build-2736575974"},"reference-count":41,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"8","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Math."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>This paper provides new bounds on the effective properties in dimension two of multiphase composites with isotropic phases having nonsymmetric conductivities. This is relevant to classical strong field magneto-transport in heterogeneous conductors with columnar microstructure, with a magnetic field in the direction of the columns. On the one hand, a polygon-like G-closure for multiphase composites without prescribed volume fractions is derived for isotropic effective resistivities. On the other hand, the G-closure of the possible average currents associated with a given applied electric field is found for anisotropic multiphase composites with prescribed volume fractions. This extends the G-closure result obtained by Ra[Formula: see text]tum and Tartar for symmetric conductivities.<\/jats:p>","DOI":"10.1137\/100798090","type":"journal-article","created":{"date-parts":[[2010,12,14]],"date-time":"2010-12-14T18:48:48Z","timestamp":1292352528000},"page":"3272-3286","source":"Crossref","is-referenced-by-count":1,"title":["New Bounds on Strong Field Magneto-Transport in Multiphase Columnar Composites"],"prefix":"10.1137","volume":"70","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":[[2010,12,14]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/PL00004242"},{"key":"R2","first-page":"47","volume":"34","author":"Alessandrini G.","year":"2009","journal-title":"Ann. Acad. Sci. Fenn. Math."},{"key":"R3","doi-asserted-by":"crossref","unstructured":"G. Allaire,\n                      Shape Optimization by the Homogenization Method\n                      , Appl. Math. Sci. 146, Springer-Verlag, New York, 2002.","DOI":"10.1007\/978-1-4684-9286-6"},{"key":"R4","unstructured":"A. Bensoussan, J. L. Lions, and G. Papanicolaou,\n                      Asymptotic Analysis for Periodic Structures\n                      , North-Holland, Amsterdam, New York, 1978."},{"key":"R5","unstructured":"D. J. Bergman,\n                      Self-duality and the low field Hall effect in\n                      2\n                      D and\n                      3\n                      D metal-insulator composites\n                      , in Percolation Structures and Processes, Annals of the Israel Physical Society, Vol. 5, G. Deutscher, R. Zallen, and J. Adler, eds., Israel Physical Society, Jerusalem, 1983, pp. 297\u2013321."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/j.physb.2006.12.032"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.71.035120"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.80.3356"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.59.2180"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.60.13016"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4371(97)00095-2"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2007.07.044"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-008-0200-y"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1137\/08073189X"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/09075901X"},{"key":"R16","doi-asserted-by":"crossref","unstructured":"A. V. Cherkaev,\n                      Variational Methods for Structural Optimization\n                      , Appl. Math. Sci. 140, Springer-Verlag, New York, 2000.","DOI":"10.1007\/978-1-4612-1188-4"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1063\/1.530782"},{"key":"R18","doi-asserted-by":"crossref","unstructured":"B. Dacorogna,\n                      Direct Methods in the Calculus of Variations\n                      , Appl. Math. Sci. 78, Springer-Verlag, Berlin, Heidelberg, 1989.","DOI":"10.1007\/978-3-642-51440-1"},{"key":"R19","first-page":"63","volume":"32","author":"Dykhne A. M.","year":"1971","journal-title":"Zh. \u00c8ksper. Teoret. Fiz., 59 (1970), pp. 110\u2013115 (in Russian); Soviet Phys. JETP"},{"key":"R20","first-page":"348","volume":"32","author":"Dykhne A. M.","year":"1971","journal-title":"Zh. \u00c8ksper. Teoret. Fiz., 59 (1970), pp. 641\u2013647 (in Russian); Soviet Phys. 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Milton,\n                      The Theory of Composites\n                      , Cambridge University Press, Cambridge, UK, 2002."},{"key":"R31","unstructured":"F. Murat,\n                      \n                        H\n                        -convergence\n                      \n                      , mimeographed notes, S\u00e9minaire d'Analyse Fonctionnelle et Num\u00e9rique, Universit\u00e9 d'Alger, Algiers, 1978 (English translation in )."},{"key":"R32","doi-asserted-by":"crossref","unstructured":"F. Murat and L. Tartar,\n                      \n                        H\n                        -convergence\n                      \n                      , in Topics in the Mathematical Modelling of Composite Materials, Progr. Nonlinear Differential Equations Appl. 31, L. Cherkaev and R. V. Kohn, eds., Birkha\u00fcser Boston, Boston, 1997, pp. 21\u201343.","DOI":"10.1007\/978-1-4612-2032-9_3"},{"key":"R33","unstructured":"M. A. Omar,\n                      Elementary Solid State Physics: Principles and Applications\n                      , World Student Series Edition, Addison\u2013Wesley, Reading, MA, 1975."},{"key":"R34","first-page":"775","volume":"19","author":"Ratum U. \u00cb.","year":"1983","journal-title":"Differentsial'nye Uravneniya, 19 (1983), pp. 1040\u20131047 (in Russian); Differ. Equ."},{"key":"R35","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.61.6288"},{"key":"R36","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.12.3368"},{"key":"R37","unstructured":"L. Tartar,\n                      Cours Peccot, Coll\u00e8ge de France\n                      , Paris, 1977, unpublished (partly written in )."},{"key":"R38","unstructured":"L. Tartar,\n                      Estimations fines des coefficients homog\u00e9n\u00e9is\u00e9s\n                      , in Ennio De Giorgi Colloquium (Paris, 1983), Res. Notes in Math. 125, P. 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