发表机构
The Hong Kong Polytechnic University; The George Washington University（香港理工大学; 乔治华盛顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一个热力学一致的多组分膜扩散界面模型，基于耦合自由能泛函和Onsager变分原理，构建了两种稳定的交替指数时间差分格式，并证明离散能量耗散，数值实验验证了蛋白质分离与膜变形。
AI 中文摘要
我们为多组分膜发展了一个热力学一致的扩散界面模型。所提出的模型源自一个耦合的自由能泛函，该泛函包含了依赖于蛋白质的弯曲弹性、扩散表面张力、体积惩罚项以及膜相关的Ohta--Kawasaki能量。应用Onsager变分原理，我们推导出一个耦合的$L^2$梯度流系统及其能量耗散律。随后，我们构建了具有Strang型组合的稳定交替ETD1格式和稳定交替ETDRK2格式（交替Strang-ETDRK2）。据我们所知，所提出的交替Strang-ETDRK2格式此前尚未针对耦合相场系统进行开发和数值分析。我们进一步在数值解的一些正则性假设下证明了两种格式的离散能量耗散。二维和三维的数值实验验证了离散能量耗散律，并展示了所提出模型产生的蛋白质分离和膜变形现象。
英文摘要
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.
Comments30 pages, 4 figures
