Continuum Limit of a Mesoscopic Model with Elasticity of Step Motion on Vicinal Surfaces
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2016-12-29
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This work considers the rigorous derivation of continuum models of step motion starting from a mesoscopic Burton–Cabrera–Frank-type model following the Xiang’s work (Xiang in SIAM J Appl Math 63(1):241–258, 2002). We prove that as the lattice parameter goes to zero, for a finite time interval, a modified discrete model converges to the strong solution of the limiting PDE with first-order convergence rate.
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Gao, Y, JG Liu and J Lu (2016). Continuum Limit of a Mesoscopic Model with Elasticity of Step Motion on Vicinal Surfaces. Journal of Nonlinear Science. pp. 1–54. 10.1007/s00332-016-9354-1 Retrieved from https://hdl.handle.net/10161/14280.
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Jian-Guo Liu
Jianfeng Lu
Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm development for problems from computational physics, theoretical chemistry, materials science, machine learning, and other related fields.
More specifically, his current research focuses include:
High dimensional PDEs; generative models and sampling methods; control and reinforcement learning; electronic structure and many body problems; quantum molecular dynamics; multiscale modeling and analysis.
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