保结构扩散域加速鞍点动力学用于润湿转变

中文摘要 AI 辅助

织构基底上的润湿转变在功能表面设计中起着核心作用，但解析其转变机制需要高效探索复杂的能量景观。特别是，鞍点对于揭示亚稳态之间的连通性和转变路径至关重要。在本工作中，我们开发了一种扩散域加速鞍点动力学（DD-ASD）框架，用于复杂织构基底上质量约束的润湿转变。扩散域公式将复杂的固体几何嵌入笛卡尔网格中，避免了在重复鞍点搜索中构建贴体网格。对相场状态和不稳定方向动力学一致地应用正交投影，在离散层面保持规定的液滴质量。将动量加速纳入鞍点动力学，以提高高阶鞍点搜索的效率。在所述的局部谱和精确特征空间假设下，我们在有效质量守恒子空间上建立了$1-\mathcal{O}(1/\sqrt{\kappa})$的局部收敛速率。数值实验证明了所提方法在解析织构基底上润湿解景观、转变路径和能量壁垒方面的有效性。我们进一步将该框架扩展到全三维润湿景观计算。

英文摘要

Wetting transitions on textured substrates play a central role in the design of functional surfaces, but resolving their transition mechanisms requires efficient exploration of complex energy landscapes. In particular, saddle points are essential for revealing the connectivity among metastable states and transition pathways. In this work, we develop a diffuse-domain accelerated saddle dynamics (DD-ASD) framework for mass-constrained wetting transitions on complex textured substrates. The diffuse-domain formulation embeds complex solid geometries into a Cartesian grid, avoiding body-fitted mesh construction in repeated saddle-point searches. An orthogonal projection is applied consistently to the phase-field state and unstable-direction dynamics, preserving the prescribed droplet mass at the discrete level. Momentum acceleration is incorporated into the saddle dynamics to improve the efficiency of high-index saddle searches. Under the stated local spectral and exact-eigenspace assumptions, we establish a local convergence rate of $1-\mathcal{O}(1/\sqrtκ)$ on the effective mass-conserving subspace. Numerical experiments demonstrate the effectiveness of the proposed method in resolving wetting solution landscapes, transition pathways, and energy barriers on textured substrates. We further extend the framework to fully three-dimensional wetting-landscape computations.

发表机构

• Nanjing Normal University（南京师范大学）
• Peking University（北京大学）

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