论文标题
结构保留轴对称两相生物膜的梯度流的离散
Structure preserving discretisations of gradient flows for axisymmetric two-phase biomembranes
论文作者
论文摘要
多相生物膜的形式和演变对于了解生活系统至关重要。为了描述这些膜，我们考虑了基于坎汉姆 - helfrich-evans两相弹性能的数学模型，这将导致涉及高度非线性边界条件的第四阶几何进化问题。我们在轴对称设置中开发了一种参数有限元方法。使用变分方法，可以为高度非线性边界价值问题得出弱制剂，以使能量衰减定律以及保护特性用于空间离散的问题。我们将证明这些属性，并表明完全离散的方案已得到良好。最后，几个数值计算表明，数值方法可用于计算复合物，实验性地观察到了两相生物膜。
The form and evolution of multi-phase biomembranes is of fundamental importance in order to understand living systems. In order to describe these membranes, we consider a mathematical model based on a Canham--Helfrich--Evans two-phase elastic energy, which will lead to fourth order geometric evolution problems involving highly nonlinear boundary conditions. We develop a parametric finite element method in an axisymmetric setting. Using a variational approach, it is possible to derive weak formulations for the highly nonlinear boundary value problems such that energy decay laws, as well as conservation properties, hold for spatially discretised problems. We will prove these properties and show that the fully discretised schemes are well-posed. Finally, several numerical computations demonstrate that the numerical method can be used to compute complex, experimentally observed two-phase biomembranes.
