arXiv subjects

Gabriele Fissore

Publications and source records attributed to Gabriele Fissore.

3 recordsLinked to original sources

arXiv2024

Geometrically constrained walls in three dimensions

We study geometrically constrained magnetic walls in a three dimensional geometry where two bulks are connected by a thin neck. Without imposing any symmetry assumption on the domain, we investigate the scaling of the energy as the size of the neck vanishes. We identify five significant scaling regimes, for all of which we characterise the energy scaling and identify the asymptotic behaviour of the domain wall. Finally, we notice the emergence of sub-regimes that are not present in the previous works due to restrictive symmetry assumptions.

math.AP↗

arXiv2024

Phase-field approximation of an epitaxial growth model with adatoms

We perform a mass constrained phase-field approximation for a model that describes the epitaxial growth of a two-dimensional thin film on a substrate in the context of linearised elasticity. The approximated model encodes a variable on the free surface of the film, that physically is interpreted as an adatom density.

math.AP↗

arXiv2024

Two dimensional graph model for epitaxial crystal growth with adatoms

We consider a model to describe stable configurations in epitaxial growth of crystals in the two dimensional case, and in the regime of linearized elasticity. The novelty is that the model also takes into consideration the adatom density on the surface of the film. These are behind the main mechanisms of crystal growth and formation of islands (or quantum dots). The main result of the paper is the integral representation of the relaxed energy.

math.AP↗