Topological analysis of the diblock copolymer equation

55. Thomas Wanner:
    Topological analysis of the diblock copolymer equation
    In: Mathematical Challenges in a New Phase of Materials Science, edited by Yasumasa Nishiura, Motoko Kotani, Springer Proceedings in Mathematics & Statistics, Vol. 166, pp. 27-51, Springer-Verlag, 2016.

Abstract

We demonstrate how topological methods can be used to study pattern formation and pattern evolution in phase-field models of materials science. In the context of the diblock copolymer model for microphase separation, we will present new quantitative results on the microstructure topology during the initial phase separation from a homogeneous state, both for a deterministic and a stochastic version of the model. We also describe the long-term dynamics of the model and associated questions of multistability, which can be addressed using rigorous topological methods aimed at determining the structure of the global attractor of the system.

Links

The published version of the paper can be found at https://doi.org/10.1007/978-4-431-56104-0_2.

Bibtex

@inproceedings{wanner:16a,
   author = {Thomas Wanner},
   title = {Topological analysis of the diblock copolymer equation},
   booktitle = {Mathematical Challenges in a New Phase of Materials Science},
   series = {Springer Proceedings in Mathematics \& Statistics},
   volume = {166},
   publisher = {Springer-Verlag},
   year = 2016,
   pages = {27--51},
   editor = {Yasumasa Nishiura and Motoko Kotani},
   doi = {10.1007/978-4-431-56104-0_2}
   }