非局域生长方程标度奇异性分析  

Analysis of the Nonlocal Growth Equations on Anomalous Scaling Behavior

作　　者：张丽萍[1,2] 张连英[1,3] 

机构地区：[1]中国矿业大学深部岩土力学与地下工程国家重点实验室,江苏徐州221116 [2]中国矿业大学理学院,江苏徐州221116 [3]徐州工程学院,江苏徐州221008

出　　处：《徐州工程学院学报（自然科学版）》2011年第1期62-67,共6页Journal of Xuzhou Institute of Technology(Natural Sciences Edition)

基　　金：国家重点基础研究发展计划项目(2007CB209400);江苏省创新学者攀登项目(BK2008007);江苏省研究生培养创新工程项目(CX09B_108Z);中国矿业大学青年基金项目(2006A043)

摘　　要：采用动力学重整化群方法,分析表面界面粗化生长动力学的标度奇异性,得到非局域生长方程动力学标度奇异指数的一般结果,并将该结果应用于非局域Kardar-Parisi-Zhang(KPZ)方程和非局域Lai-Das Sarma-Villain(LDV)方程,以判断其标度奇异性.研究结果表明:生长方程的动力学标度奇异性除了与基底维数、最相关项有关外,还与非局域因子密切相关,局域条件下表现为正常标度行为,而非局域情况下出现奇异标度行为.A dynamic renormalization-group method is generalized to explore the anomalously dynamic scaling property of kinetic roughening growth equation and the general conclusion of the anomalous exponents of the nonlocal growth equation is drawn. These results of the anomalous exponents are employed in several typical nonlocal growth equations,which are the nonlocal Kardar-Parisi-Zhang（KPZ）equation and nonlocal Lai-Das Sarma-Villain（LDV） equation, to judge the condition of anomalous scaling behaviors. Analyses show that within the long wavelength limit the dynamic scaling property of a growth equation is relative to the nonlocal factor as well as the dimension of the system and the most relative term, and if anomalous scaling of the equation exists, super roughening instead of intrinsic anomalous roughening will be displayed in local growth models.

关 键 词：非局域生长方程 标度奇异性 动力学重整化群理论 

分 类 号：O414.22[理学—理论物理]