On differentiability of the membrane-mediated mechanical interaction energy of discrete-continuum membrane-particle models

DOI10.4171/IFB/461MaRDI QIDQ2077421

Carsten Gräser, Tobias Kies

Publication date: 21 February 2022

Published in: Interfaces and Free Boundaries (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.11192

zbMATH Keywords

well-posednessinteraction energytopology optimizationbiomembraneCanham-Helfrich modelLax-Milgram's theoremmembrane-particle system

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite difference methods applied to problems in solid mechanics (74S20) Membranes (74K15) Biomechanical solid mechanics (74L15) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Optimization of shapes other than minimal surfaces (49Q10) Cell biology (92C37) Free boundary problems for PDEs (35R35) PDEs in connection with mechanics of deformable solids (35Q74) Integro-partial differential equations (35R09)

Related Items (1)

A formula for membrane mediated point particle interactions on near spherical biomembranes

Cites Work

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• A variational approach to particles in lipid membranes
• Small deformations of Helfrich energy minimising surfaces with applications to biomembranes
• Discretization error estimates for penalty formulations of a linearized Canham–Helfrich-type energy
• Ordinary Differential Equations

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