The Dynamics of Nucleation in Stochastic Cahn-Morral Systems

被引:16
作者
Desi, Jonathan P. [1 ]
Edrees, Hanein H. [2 ]
Price, Joseph J. [2 ]
Sander, Evelyn [2 ]
Wanner, Thomas [2 ]
机构
[1] Univ Maryland Baltimore Cty, Dept Math & Stat, Baltimore, MD 21250 USA
[2] George Mason Univ, Dept Math Sci, Fairfax, VA 22030 USA
基金
美国国家科学基金会;
关键词
Cahn-Morral systems; nucleation; stochastic partial differential equation; domain exit; SPINODAL DECOMPOSITION; HILLIARD EQUATION; NONUNIFORM SYSTEM; FREE ENERGY; HIGHER DIMENSIONS; MOTION;
D O I
10.1137/100801378
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Cahn-Morral systems serve as models for several phase separation phenomena in multicomponent alloys. In this paper we study the dynamical aspects of nucleation in a stochastic version of these models using numerical simulations, concentrating on ternary, i.e., three-component, alloys on two-dimensional square domains. We perform numerical studies and give a statistical classification for the distribution of droplet types as the component structure of the alloy is varied. We relate these statistics to the low-energy equilibria of the deterministic equation.
引用
收藏
页码:707 / 743
页数:37
相关论文
共 42 条
[1]  
Adams R. A., 1978, SOBOLEV SPACES
[2]  
[Anonymous], ELECT J DIFF EQNS
[3]  
[Anonymous], 1893, Verh. Konink. Akad. Wetensch. Amsterdam
[4]   THE DYNAMICS OF NUCLEATION FOR THE CAHN-HILLIARD EQUATION [J].
BATES, PW ;
FIFE, PC .
SIAM JOURNAL ON APPLIED MATHEMATICS, 1993, 53 (04) :990-1008
[5]   Second phase spinodal decomposition for the Cahn-Hilliard-Cook equation [J].
Bloemker, Dirk ;
Maier-Paape, Stanislaus ;
Wanner, Thomas .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 360 (01) :449-489
[6]   NUCLEATION IN THE ONE-DIMENSIONAL STOCHASTIC CAHN-HILLIARD MODEL [J].
Bloemker, Dirk ;
Gawron, Bernhard ;
Wanner, Thomas .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2010, 27 (01) :25-52
[7]   Spinodal decomposition for the Cahn-Hilliard-Cook equation [J].
Blömker, D ;
Maier-Paape, S ;
Wanner, T .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2001, 223 (03) :553-582
[8]  
Blomker D., 2001, Stoch. Dyn., V1, P239
[9]  
Blomker Dirk., 2005, MATH METHODS MODELS, P1
[10]   FREE ENERGY OF A NONUNIFORM SYSTEM .2. THERMODYNAMIC BASIS [J].
CAHN, JW .
JOURNAL OF CHEMICAL PHYSICS, 1959, 30 (05) :1121-1124