caa a22 4500 605515972 CHVBK 20210128100712.0 cr unu---uuuuu 210128e20151101xx s 000 0 eng 10.1007/s00205-015-0873-y doi (NATIONALLICENCE)springer-10.1007/s00205-015-0873-y Domain Formation in Magnetic Polymer Composites: An Approach Via Stochastic Homogenization [Elektronische Daten] [Roberto Alicandro, Marco Cicalese, Matthias Ruf] We study the magnetic energy of magnetic polymer composite materials as the average distance between magnetic particles vanishes. We model the position of these particles in the polymeric matrix as a stochastic lattice scaled by a small parameter ɛ and the magnets as classical $${\pm 1}$$ ± 1 spin variables interacting via an Ising type energy. Under surface scaling of the energy we prove, in terms of Γ-convergence, that, up to subsequences, the (continuum) Γ-limit of these energies is finite on the set of Caccioppoli partitions representing the magnetic Weiss domains where it has a local integral structure. Assuming stationarity of the stochastic lattice, we can make use of ergodic theory to further show that the Γ-limit exists and that the integrand is given by an asymptotic homogenization formula which becomes deterministic if the lattice is ergodic. Springer-Verlag Berlin Heidelberg, 2015 Alicandro Roberto DIEI, Università di Cassino e del Lazio meridionale, via Di Biasio 43, 03043, Cassino (FR), Italy aut Cicalese Marco Zentrum Mathematik-M7, Technische Universität München, Boltzmannstrasse 3, 85748, Garching, Germany aut Ruf Matthias Zentrum Mathematik-M7, Technische Universität München, Boltzmannstrasse 3, 85748, Garching, Germany aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/2(2015-11-01), 945-984 0003-9527 218:2<945 2015 218 205 https://doi.org/10.1007/s00205-015-0873-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-015-0873-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Alicandro Roberto DIEI, Università di Cassino e del Lazio meridionale, via Di Biasio 43, 03043, Cassino (FR), Italy aut NATIONALLICENCE 700 1- Cicalese Marco Zentrum Mathematik-M7, Technische Universität München, Boltzmannstrasse 3, 85748, Garching, Germany aut NATIONALLICENCE 700 1- Ruf Matthias Zentrum Mathematik-M7, Technische Universität München, Boltzmannstrasse 3, 85748, Garching, Germany aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/2(2015-11-01), 945-984 0003-9527 218:2<945 2015 218 205