A Thermodynamically Consistent Model for Multicomponent Vesicles
Abstract
We develop a thermodynamically consistent diffuse-interface model for multicomponent membranes. The proposed model is derived from a coupled free energy functional that incorporates protein-dependent bending elasticity, diffuse surface tension, a volume penalty, and a membrane-associated Ohta--Kawasaki energy. Applying the Onsager variational principle, we derive a coupled L2 gradient flow system and its energy dissipation law. We then construct a stabilized alternating ETD1 scheme and a stabilized alternating ETDRK2 scheme with Strang-type composition (alternating Strang-ETDRK2). To the best of our knowledge, the proposed alternating Strang-ETDRK2 scheme has not previously been developed and analyzed for coupled phase field systems. We further prove the discrete energy dissipation for both schemes under some regularity assumptions on the numerical solutions. Numerical experiments in two and three dimensions validate the discrete energy dissipation law, and present the protein segregation and membrane deformation produced by the proposed model.
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BibTeX
@misc{luo2026thermodynamically,
title = {{A Thermodynamically Consistent Model for Multicomponent Vesicles}},
author = {Wangbo Luo and Zhonghua Qiao and Yanxiang Zhao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10168},
eprint = {2609.10168},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10168},
}
RIS
TY - UNPB
TI - A Thermodynamically Consistent Model for Multicomponent Vesicles
AU - Wangbo Luo
AU - Zhonghua Qiao
AU - Yanxiang Zhao
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10168
UR - https://arxiv.org/abs/2609.10168
AB - We develop a thermodynamically consistent diffuse-interface model for multicomponent membranes. The proposed model is derived from a coupled free energy functional that incorporates protein-dependent bending elasticity, diffuse surface tension, a volume penalty, and a membrane-associated Ohta--Kawasaki energy. Applying the Onsager variational principle, we derive a coupled L^2 gradient flow system and its energy dissipation law. We then construct a stabilized alternating ETD1 scheme and a stabilized alternating ETDRK2 scheme with Strang-type composition (alternating Strang-ETDRK2). To the best of our knowledge, the proposed alternating Strang-ETDRK2 scheme has not previously been developed and analyzed for coupled phase field systems. We further prove the discrete energy dissipation for both schemes under some regularity assumptions on the numerical solutions. Numerical experiments in two and three dimensions validate the discrete energy dissipation law, and present the protein segregation and membrane deformation produced by the proposed model.
ER -