MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Multiscale Modeling of Materials - the Role of Analysis

Sergio Conti, Antonio DeSimone, Georg Dolzmann, Stefan Müller and Felix Otto


We present two case studies how analysis can be used to derive a hierarchy of models to capture multiscale behavior of materials. The determination, via Gamma-convergence, of the thin film limit of micromagnetism delivers a reduced two-dimensional model for soft ferromagnetic films which justifies previously known theories for small fields and extends them to the regime of field penetration. The analytic evaluation of the quasiconvex envelope of the microscopic energy density of nematic elastomers allows efficient numerical computations with finite elements and shows the existence of a new "smectic" phase. In both cases, the numerical solution of the coarse-grained model is complemented by a reconstruction of the microscopic pattern associated with the reduced field.


Related publications

2003 Repository Open Access
Sergio Conti, Antonio DeSimone, Georg Dolzmann, Stefan Müller and Felix Otto

Multiscale modeling of materials : the role of analysis

In: Trends in nonlinear analysis / Markus Kirkilionis... (eds.)
Berlin [u. a.] : Springer, 2003. - pp. 375-408