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Microstructures and Anti-phase Boundaries in Long-range Lattice Systems by Braides, Andrea; Voglino, Edoardo; Zanardini, Matteo is a scholarly article available to read on EtoBox.

What is Microstructures and Anti-phase Boundaries in Long-range Lattice Systems about?

We study the effect of long-range interactions in non-convex one-dimensional lattice systems in the simplified yet meaningful assumption that the relevant long-range interactions are between $M$-neighbours for some $M\ge 2$ and are convex. If short-range interactions are non-convex we then have a competition between short-range oscillations and long-range ordering. In the case of a double-well nearest-neighbour potential, thanks to a recent result by Braides, Causin, Solci and Truskinovsky, we are able to show that such a competition generates $M$-periodic minimizers whose arrangements are driven by an interfacial energy. Given $M$, the shape of such minimizers is universal, and independent of the details of the energies, but the number and shapes of such minimizers increases as $M$ diverges.

Author

Braides, Andrea; Voglino, Edoardo; Zanardini, Matteo

Published

2024

Language

EN