Overhanging of membranes and filaments adhering to periodic graph substrates

TL;DR

This paper analyzes the behavior of membranes and filaments adhering to periodic graph substrates, providing conditions for their configurations and demonstrating cases where overhanging structures are inevitable.

Contribution

It introduces a mathematical framework for membranes and filaments on periodic substrates and identifies conditions leading to overhanging configurations.

Findings

Global minimizers can be represented as graphs under certain conditions.

Overhanging configurations occur in specific situations.

The study provides criteria for when overhanging is unavoidable.

Abstract

This paper mathematically studies membranes and filaments adhering to periodic patterned substrates in a one-dimensional model. The problem is formulated by the minimizing problem of an elastic energy with a contact potential on graph substrates. Global minimizers (ground states) are mainly considered in view of their graph representations. Our main results exhibit sufficient conditions for the graph representation and examples of situations where any global minimizer must overhang.