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Computing the volume enclosed by a periodic surface and its variation to model a follower pressure
Rahimi Lenji, Mohammad; Zhang, Kuan; Arroyo Balaguer, Marino
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria
In modeling and numerically implementing a follower pressure in a geometrically nonlinear setting, one needs to compute the volume enclosed by a surface and its variation. For closed surfaces, the volume can be expressed as a surface integral invoking the divergence theorem. For periodic systems, widely used in computational physics and materials science, the enclosed volume calculation and its variation is more delicate and has not been examined before. Here, we develop simple expressions involving integrals on the surface, on its boundary lines, and point contributions. We consider two specific situations, a periodic tubular surface and a doubly periodic surface enclosing a volume with a nearby planar substrate, which are useful to model systems such as pressurized carbon nanotubes, supported lipid bilayers or graphene. We provide a set of numerical examples, which show that the familiar surface integral term alone leads to an incorrect volume evaluation and spurious forces at the periodic boundaries.
Peer Reviewed
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
Periodic surface
Volume
Pressure
Follower load
GRAPHENE
MEMBRANES
ADHESION
TRENDS
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