论文标题
部分可观测时空混沌系统的无模型预测
Phase field modeling and computation of vesicle growth or shrinkage
论文作者
论文摘要
我们提出了一个相位场模型，用于由于化学势梯度引起的渗透压引起的囊泡生长或收缩。该模型由描述相场演化的艾伦 - 卡纳方程和描述浓度场演化的cahn-hilliard方程组成。我们通过常见的切线结构建立了囊泡生长或收缩的控制条件。在膜变形过程中，该模型确保总质量保护并满足表面积约束。我们开发了一个非线性数值方案，即非线性高斯 - seidel弛豫算子和V-Cycles Multigrid求解器的组合，用于计算2D囊泡的平衡形状。收敛测试确认$ \ MATHCAL {O}（T+H^2）$精度。数值结果表明，扩散界面模型捕获了动力学的主要特征：对于生长的囊泡，如果整个膜上的浓度差和初始渗透压足够大，则存在圆形的平衡形状；在收缩囊泡的同时，存在丰富的手指样平衡形态。
We present a phase field model for vesicle growth or shrinkage induced by an osmotic pressure due to a chemical potential gradient. The model consists of an Allen-Cahn equation describing the evolution of phase field and a Cahn-Hilliard equation describing the evolution of concentration field. We establish control conditions for vesicle growth or shrinkage via a common tangent construction. During the membrane deformation, the model ensures total mass conservation and satisfies surface area constraint. We develop a nonlinear numerical scheme, a combination of nonlinear Gauss-Seidel relaxation operator and a V-cycles multigrid solver, for computing equilibrium shapes of a 2D vesicle. Convergence tests confirm an $\mathcal{O}(t+h^2)$ accuracy. Numerical results reveal that the diffuse interface model captures the main feature of dynamics: for a growing vesicle, there exist circle-like equilibrium shapes if the concentration difference across the membrane and the initial osmotic pressure are large enough; while for a shrinking vesicle, there exists a rich collection of finger-like equilibrium morphologies.
