graphene deposited over a trench 
 has been studied in the context of nanomechanical resonators , where 
 experiments indicate adhesion of the graphene sheet to the trench 
 boundary and sidewalls leads to self - tensioning ; however , this adhesion 
 is not well understood . 
 we use molecular dynamics to simulate graphene 
 deposited on a trench and study how adhesion to the sidewalls depends 
 on substrate interaction , temperature , and curvature of the edge of 
 the trench . over the range of parameters we study , 
 the depth at the 
 center of the sheet is approximately linear in substrate interaction 
 strength and temperature but not trench width , and we explain this 
 using a one - dimensional model for the sheet configuration .