Geometrical evolution laws are widely used in continuum modeling of surface and interface motion in materials science.In this article,we first give a brief review of various kinds of geometrical evolution laws and the...Geometrical evolution laws are widely used in continuum modeling of surface and interface motion in materials science.In this article,we first give a brief review of various kinds of geometrical evolution laws and their variational derivations,with an emphasis on strong anisotropy.We then survey some of the finite element based numerical methods for simulating the motion of interfaces focusing on the field of thin film growth.We discuss the finite element method applied to front-tracking,phase-field and level-set methods.We describe various applications of these geometrical evolution laws to materials science problems,and in particular,the growth and morphologies of thin crystalline films.展开更多
基金The work of B.Li was supported by the US National Science Foundation(NSF)through grants DMS-0451466 and DMS-0811259the US Department of Energy through grant DE-FG02-05ER25707+2 种基金the Center for Theoretical Biological Physics through the NSF grants PHY-0216576 and PHY-0822283J.Lowengrub gratefully acknowledges support from the US National Science Foundation Divisions of Mathematical Sciences(DMS)and Materials Research(DMR)The work of A.Voigt and A.Ratz was supported by the 6th Framework program of EU STRP 016447 and German Science Foundation within the Collaborative Research Program SFB 609.
文摘Geometrical evolution laws are widely used in continuum modeling of surface and interface motion in materials science.In this article,we first give a brief review of various kinds of geometrical evolution laws and their variational derivations,with an emphasis on strong anisotropy.We then survey some of the finite element based numerical methods for simulating the motion of interfaces focusing on the field of thin film growth.We discuss the finite element method applied to front-tracking,phase-field and level-set methods.We describe various applications of these geometrical evolution laws to materials science problems,and in particular,the growth and morphologies of thin crystalline films.
