Deposition, diffusion, and nucleation on an interval

نویسندگان

چکیده

Motivated by nanoscale growth of ultra-thin films, we study a model deposition, on an interval substrate, particles that perform Brownian motions until any two meet, when they nucleate to form static island, which acts as absorbing barrier subsequent particles. This is continuum version lattice studied in the applied literature. We show associated interval-splitting process converges sparse deposition limit Markovian (in vein Brennan and Durrett) governed splitting density with compact Fourier series expansion but, apparently, no simple closed form. same governs fixed rate, large time asymptotics normalized gap distribution, so these are independent rate. The derived solving exit problem for planar motion from right-angled triangle, extending work Smith Watson.

منابع مشابه

Island nucleation and growth with anomalous diffusion.

While most studies of submonolayer island nucleation and growth have been based on the assumption of ordinary monomer diffusion corresponding to diffusion exponent μ=1, in some cases either subdiffusive (μ<1) or superdiffusive (μ>1) behavior may occur. Here we present general expressions for the exponents describing the flux dependence of the island and monomer densities as a function of the cr...

متن کامل

an investigation of the impact of self monitoring on langauge teachers motivational practice and its effect on learners motivation

the central purpose of this study was to conduct a case study about the role of self monitoring in teacher’s use of motivational strategies. furthermore it focused on how these strategies affected students’ motivational behavior. although many studies have been done to investigate teachers’ motivational strategies use (cheng & d?rnyei, 2007; d?rnyei & csizer, 1998; green, 2001, guilloteaux & d?...

Nucleation and strain-stabilization during organic semiconductor thin film deposition

The nucleation mechanisms during solution deposition of organic semiconductor thin films determine the grain morphology and may influence the crystalline packing in some cases. Here, in-situ optical spectromicroscopy in reflection mode is used to study the growth mechanisms and thermal stability of 6,13-bis(trisopropylsilylethynyl)-pentacene thin films. The results show that the films form in a...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Annals of Applied Probability

سال: 2022

ISSN: ['1050-5164', '2168-8737']

DOI: https://doi.org/10.1214/22-aap1804