Year: 2024
Type: article
Abstract: We study energy scaling laws for a simplified, singularly perturbed, double-well nucleation problem confined in a half-space, in the absence of gauge invariance and for an inclusion of fixed volume. Motivated by models for boundary nucleation of a single-phase martensite inside a parental phase of austenite, our main focus in this nonlocal isoperimetric problem is how the relationship between the rank-1 direction and the orientation of the half-space influences the energy scaling with respect to the fixed volume of the inclusion. Up to prefactors depending on this relative orientation, the scaling laws coincide with the corresponding ones for bulk nucleation (Knüpfer in Proc R Soc A Math Phys Eng Sci 467(2127): 695-717, 2011) for all rank-1 directions, but the ones normal to the confining hyperplane, where the scaling is as in a three-gradient problem in full space, resulting in a lower energy barrier (Rüland et al. J Nonlinear Sci 33(2): 25 2023).
Authors: Antonio Tribuzio, Konstantinos Zemas
Institution: University of Bonn
Language: English
Subfield: Materials Chemistry
Field: Materials Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Awards: EXC 2047: Hausdorff Center for Mathematics (HCM), G1600773818, EXC 2044: Mathematik Münster: Dynamik – Geometrie – Struktur, G4093683979, G4274133347, G546635654, G6938060324, Regularität und Skalierung von wilden Mikrostrukturen in der Modellierung von Formgedächtnismaterialien, G8923514526
OpenAlex ID: W4404532941