Publication 21-CNA-009
Global and local energy minimizers for a nanowire growth model
Irene Fonseca
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
fonseca@andrew.cmu.edu
Nicola Fusco
Dipartimento di Matematica e Applicazioni "R. Caccioppoli"
Università degli Studi di
Napoli "Federico II"
Napoli, Italy
n.fusco@unina.it
Giovanni Leoni
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
giovanni@andrew.cmu.edu
Massimiliano Morini
Dipartimento di Scienze Matematiche, Fisiche e Informatiche
Università degli Studi di Parma
Parma, Italy
massimiliano.morini@unipr.it
Abstract: We consider a model for vapor-liquid-solid growth of nanowires proposed in the physical literature. Liquid drops are described as local or global volume-constrained minimizers of the capillarity energy outside a semi-infinite convex obstacle modeling the nanowire. We first
address the existence of global minimizers and then, in the case of rotationally symmetric nanowires, we investigate how the presence of a sharp edge affects the shape of local minimizers and the validity of Young's law.
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