Newton-Cartan submanifolds and fluid membranes

Area of Science:

• Geometric description of submanifolds
• Theoretical physics
• Fluid dynamics

Background:

• Galilean-invariant hydrodynamics requires a covariant spacetime formulation.
• Fluid membranes and lipid vesicles are crucial in biological and physical systems.
• Understanding thermal equilibrium and dynamics of membranes is key.

Purpose of the Study:

• To develop a geometric description of submanifolds in Newton-Cartan spacetime.
• To establish a covariant spacetime formulation for Galilean-invariant hydrodynamics on curved surfaces.
• To study fluid membranes in thermal equilibrium and their dynamics.

Main Methods:

• Developing geometric descriptions of submanifolds within Newton-Cartan spacetime.
• Formulating Galilean-invariant hydrodynamics covariantly on curved surfaces.
• Modeling fluid membranes based on surface tension and extracting stresses.

Main Results:

• Established a geometric framework for fluid membranes in curved spacetimes.
• Demonstrated that perturbations from equilibrium yield standard elastic wave dispersion.
• Derived a generalized Canham-Helfrich bending energy for lipid vesicles.

Conclusions:

• The developed geometric framework is suitable for studying fluid membranes.
• The model accurately predicts elastic wave behavior and generalizes bending energy for lipid vesicles.
• This work provides a foundation for understanding thermal equilibrium and dynamics of membranes.