论文标题
间隔的沉积，扩散和成核
Deposition, diffusion, and nucleation on an interval
论文作者
论文摘要
通过超薄膜的纳米级生长的促进，我们研究了一种在间隔基板上进行的沉积模型，该模型的颗粒的颗粒会进行布朗运动，直到任何两个动作都会遇到，当它们成核形成一个静态岛，该岛屿是对后续颗粒的吸收性障碍。这是应用文献中研究的晶格模型的连续版本。我们表明，相关的间隔分解过程以稀疏沉积极限收敛到马尔可夫过程（Brennan和Durrett的静脉），该过程由分裂密度管理，并具有紧凑的傅立叶串联膨胀，但显然没有简单的封闭形式。我们表明，相同的分裂密度控制了固定沉积速率，归一化间隙分布的较大时间渐近性，因此这些渐进性与沉积速率无关。分裂密度是通过从右角三角形的平面布朗运动的出口问题来得出的，从而扩展了史密斯和沃森的作品。
Motivated by nanoscale growth of ultra-thin films, we study a model of deposition, on an interval substrate, of particles that perform Brownian motions until any two meet, when they nucleate to form a static island, which acts as an absorbing barrier to subsequent particles. This is a continuum version of a lattice model studied in the applied literature. We show that the associated interval-splitting process converges in the sparse deposition limit to a Markovian process (in the vein of Brennan and Durrett) governed by a splitting density with a compact Fourier series expansion but, apparently, no simple closed form. We show that the same splitting density governs the fixed deposition rate, large time asymptotics of the normalized gap distribution, so these asymptotics are independent of deposition rate. The splitting density is derived by solving an exit problem for planar Brownian motion from a right-angled triangle, extending work of Smith and Watson.
