论文标题
固态润湿和脱水的微观依据
Microscopical justification of Solid-State Wetting and Dewetting
论文作者
论文摘要
与冬季问题有关的连续模型，即，确定属于底物上的晶体滴剂的平衡形状的问题是通过严格的离散到continuum通过$γ$ convergence convergence convergence convergence contomist of the Atomic相互作用的掉液和定义的，这是通过$γ$ convergence convergence converne contections of the proptivations of the proppers of to drop of to drop of sopprodes of soseftip的均可量，并以固定的相互作用，以固定的相互作用和固定的相互作用。作为分析的副产品，滴表面各向异性和连续模型中出现的滴度/底物粘附参数的有效表达式是根据原子电位来表征的，这些原子电位是由Heitmann-Radin粘性盘类型选择的。此外，仅取决于此类电势的阈值条件可以区分润湿状态，在该方案中，离散的最小化器被明确表征为具有一个原子厚度的层中包含的构型，即，即在基材料上的润湿层，与脱水方案。在后一种制度中，鉴于原子数量倾向于无穷大的质量保护，因此原子模型的最小化量表的适当尺度会融合（直至提取底物表面上的子序列和表现翻译），以使冬季茶几的限制性最小化尺寸的最小化尺度满足体积结构的限制。
The continuum model related to the Winterbottom problem, i.e., the problem of determining the equilibrium shape of crystalline drops resting on a substrate, is derived in dimension two by means of a rigorous discrete-to-continuum passage by $Γ$-convergence of atomistic models taking into consideration the atomic interactions of the drop particles both among themselves and with the fixed substrate atoms. As a byproduct of the analysis effective expressions for the drop surface anisotropy and the drop/substrate adhesion parameter appearing in the continuum model are characterized in terms of the atomistic potentials, which are chosen of Heitmann-Radin sticky-disc type. Furthermore, a threshold condition only depending on such potentials is determined distinguishing the wetting regime, where discrete minimizers are explicitly characterized as configurations contained in a layer with a one-atom thickness, i.e., the wetting layer, on the substrate, from the dewetting regime. In the latter regime, also in view of a proven conservation of mass in the limit as the number of atoms tends to infinity, proper scalings of the minimizers of the atomistic models converge (up to extracting a subsequence and performing translations on the substrate surface) to a bounded minimizer of the Winterbottom continuum model satisfying the volume constraint.
