Newton{Cartan Submanifolds and Fluid Membranes

Jay Armas, Jelle Hartong, Emil Have, Bjarke F. Nielsen, Niels A. Obers

Research output: Contribution to journalArticlepeer-review

Abstract

We develop the geometric description of submanifolds in Newton-Cartan spacetime. This provides the necessary starting point for a covariant spacetime formulation of Galilean-invariant hydrodynamics on curved surfaces. We argue that this is the natural geometrical framework to study fluid membranes in thermal equilibrium and their dynamics out of equilibrium. A simple model of fluid membranes that only depends on the surface tension is presented and, extracting the resulting stresses, we show that perturbations away from equilibrium yield the standard result for the dispersion of elastic waves. We also find a generalization of the Canham-Helfrich bending energy for lipid vesicles that takes into account the requirements of thermal equilibrium.
Original languageEnglish
Number of pages56
JournalPhysical Review E
Volume101
Issue number6
DOIs
Publication statusPublished - 18 Jun 2020

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