Crystal lattice deformations can be described microscopically by explicitly accounting for the position of atoms or macroscopically by continuum elasticity.In this work,we report on the description of continuous elast...Crystal lattice deformations can be described microscopically by explicitly accounting for the position of atoms or macroscopically by continuum elasticity.In this work,we report on the description of continuous elastic fields derived from an atomistic representation of crystalline structures that also include features typical of the microscopic scale.Analytic expressions for strain components are obtained from the complex amplitudes of the Fourier modes representing periodic lattice positions,which can be generally provided by atomistic modeling or experiments.The magnitude and phase of these amplitudes,together with the continuous description of strains,are able to characterize crystal rotations,lattice deformations,and dislocations.Moreover,combined with the so-called amplitude expansion of the phase-field crystal model,they provide a suitable tool for bridging microscopic to macroscopic scales.This study enables the in-depth analysis of elasticity effects for macroscale and mesoscale systems taking microscopic details into account.展开更多
We derive and numerically solve a surface active nematodynamics model.We validate the numerical approach on a sphere and analyse the influence of hydro-dynamics on the oscillatory motion of topological defects.For ell...We derive and numerically solve a surface active nematodynamics model.We validate the numerical approach on a sphere and analyse the influence of hydro-dynamics on the oscillatory motion of topological defects.For ellipsoidal surfaces the influence of geometric forces on these motion patterns is addressed by taking into ac-count the effects of intrinsic as well as extrinsic curvature contributions.The numerical experiments demonstrate the stronger coupling with geometric properties if extrinsic curvature contributions are present and provide a possibility to tuneflow and defect motion by surface properties.展开更多
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M.S.acknowledges the support of the Postdoctoral Research Fellowship awarded by the Alexander von Humboldt FoundationA.V.acknowledges support from the German Research Foundation under Grant no.Vo899/20 within SPP 1959K.R.E.acknowledges financial support from the National Science Foundation under Grant No.DMR1506634.
文摘Crystal lattice deformations can be described microscopically by explicitly accounting for the position of atoms or macroscopically by continuum elasticity.In this work,we report on the description of continuous elastic fields derived from an atomistic representation of crystalline structures that also include features typical of the microscopic scale.Analytic expressions for strain components are obtained from the complex amplitudes of the Fourier modes representing periodic lattice positions,which can be generally provided by atomistic modeling or experiments.The magnitude and phase of these amplitudes,together with the continuous description of strains,are able to characterize crystal rotations,lattice deformations,and dislocations.Moreover,combined with the so-called amplitude expansion of the phase-field crystal model,they provide a suitable tool for bridging microscopic to macroscopic scales.This study enables the in-depth analysis of elasticity effects for macroscale and mesoscale systems taking microscopic details into account.
基金financial support by DFG through FOR3013,computing resources provided by PFAMDIS at FZ Julich.
文摘We derive and numerically solve a surface active nematodynamics model.We validate the numerical approach on a sphere and analyse the influence of hydro-dynamics on the oscillatory motion of topological defects.For ellipsoidal surfaces the influence of geometric forces on these motion patterns is addressed by taking into ac-count the effects of intrinsic as well as extrinsic curvature contributions.The numerical experiments demonstrate the stronger coupling with geometric properties if extrinsic curvature contributions are present and provide a possibility to tuneflow and defect motion by surface properties.
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.
