分数阶随机动力学生长过程的非局域效应研究

项目名称： 分数阶随机动力学生长过程的非局域效应研究

项目编号： No.11247029

项目类型： 专项基金项目

立项/批准年度： 2013

项目学科： 物理学II

项目作者： 夏辉

作者单位： 中国矿业大学

项目金额： 20万元

中文摘要： 本项目对分数阶随机动力学生长过程的非局域效应进行理论探索，研究的内容主要包括：i)采用数值方法分别对Langevin类型的非局域动力学方程进行模拟，通过对表面粗糙度和高度差关联函数等物理量的定量分析，探讨非局域生长过程呈现动力学标度行为的物理机制；ii)应用自洽展开理论、直接标度分析等解析近似方法研究描述表面粗糙生长的非局域随机微分方程的动力学标度性质，通过对表面生长结构因子、局域梯度等特征量的计算，标定出非局域效应对生长动力学行为的影响； iii)采用动态蒙特卡洛方法对与连续性生长方程相对应的离散生长模型进行模拟，考虑遮蔽效应、长程关联等非局域因素对生长动力学行为的作用。本项目的研究意义在于：结合非平衡统计方法与分数阶微积分理论研究随机生长过程的非局域效应，将有助于为生长动力学行为提供较合理的理论解释，加深和完善相关的理论。

中文关键词： 非平衡动力学系统；分数阶生长模型；非局域效应；标度行为；

英文摘要： The nonlocal effects in the fractional stochastic dynamic growth processes will be investigated theoretically. The main contents of this project are as follows: i) The Langevin-type nonlocal dynamic equations will be studied by means of numerical simulations, and the physical mechanisms of the dynamic scaling behavior in the nonlocal growth processes will be explored by calculating the surface roughness and the height difference correlation function; ii) Based on analytical approximation methods including self-consistent expansion and scaling analysis, the dynamic scaling properties of the nonlocal stochastic differential equations describing surface roughness growth will be investigated, and the influence of nonlocal effects on the growth dynamic behavior will be analyzed through the characteristic quantities, such as structure factor and local slope; iii) The discrete nonlocal growth models corresponding with the continuum growth equations will be preformed using kinetic Monte Carlo method, the influence of nonlocal factors including shadowing effects and long-range correlation on growth dynamic behavior will be considered. The research significance of the project will help, by combination of nonequilibrium statistical method and fractional differential calculus to study nonlocal effects in the stochastic grow

英文关键词： nonequilibrium dynamic system；fractional growth model；nonlocal effects；scaling behavior；