论文标题
在近场两相生物膜的相位场模型的尖锐界面限制上
On the sharp interface limit of a phase field model for near-spherical two phase biomembranes
论文作者
论文摘要
我们认为，对于涉及局部平均曲率与第一和第二作者提出的局部组成之间耦合的两个相的两个相的相位场模型，我们考虑了尖锐的界面渐变渐变。该模型是由脂质筏形成动机的。我们仅根据膜成分引入减少的扩散界面能量，并得出$γ-$限制。我们证明了极限功能和尖锐界面能量重合的Euler-Lagrange方程。最后，我们考虑了一个梯度流程方程的系统，该梯度流动方程具有相位场模型的保守艾伦-CAHN动力学。进行形式的渐近分析，我们获得了一个尖锐界面能量耦合的梯度流程方程系统，用于相位界面到第四阶PDE PDE自由边界问题，以实现表面变形。
We consider sharp interface asymptotics for a phase field model of two phase near spherical biomembranes involving a coupling between the local mean curvature and the local composition proposed by the first and second authors. The model is motivated by lipid raft formation. We introduce a reduced diffuse interface energy depending only on the membrane composition and derive the $Γ-$limit. We demonstrate that the Euler-Lagrange equations for the limiting functional and the sharp interface energy coincide. Finally, we consider a system of gradient flow equations with conserved Allen-Cahn dynamics for the phase field model. Performing a formal asymptotic analysis we obtain a system of gradient flow equations for the sharp interface energy coupling geodesic curvature flow for the phase interface to a fourth order PDE free boundary problem for the surface deformation.
