Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method
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TLDR
This paper develops a first and second order time-stepping scheme based on the “Invariant Energy Quadratization” (IEQ) method, and proves that all proposed schemes are unconditionally energy stable.About:
This article is published in Journal of Computational Physics.The article was published on 2017-03-15 and is currently open access. It has received 253 citations till now. The article focuses on the topics: Temporal discretization & Linear system.read more
Citations
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The scalar auxiliary variable (SAV) approach for gradient flows
TL;DR: Numerical results are presented to show that the accuracy and effectiveness of the SAV approach over the existing methods are superior.
Journal ArticleDOI
Numerical Approximations for a three components Cahn-Hilliard phase-field Model based on the Invariant Energy Quadratization method
TL;DR: In this paper, a set of first-and second-order temporal approximation schemes based on a novel "Invariant Energy Quadratization" approach is presented. But the scheme is not energy stable.
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Numerical approximations for a phase field dendritic crystal growth model based on the invariant energy quadratization approach
TL;DR: In this article, the authors proposed a semi-discrete scheme for phase field dendritic crystal growth, which is derived from the variation of a free energy functional, consisting of a temperature dependent bulk potential and a conformational entropy with a gradient-dependent anisotropic coefficient.
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A novel linear second order unconditionally energy stable scheme for a hydrodynamic Q -tensor model of liquid crystals
TL;DR: A novel, linear, second order semi-discrete scheme in time to solve the governing system of equations in the hydrodynamic Q -tensor model, developed following the novel ‘ energy quadratization ’ strategy so that it is linear and unconditionally energy stable at the semi- Discrete level.
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Linear and unconditionally energy stable schemes for the binary fluid–surfactant phase field model
Xiaofeng Yang,Lili Ju +1 more
TL;DR: In this article, the authors considered the numerical solution of a binary fluid-surfactant phase field model, in which the free energy contains a nonlinear coupling entropy, a Ginzburg-Landau double well potential, and a logarithmic Flory-Huggins potential.
References
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Book
Molecular theory of capillarity
John S. Rowlinson,B. Widom +1 more
TL;DR: The theory of Van Der Waals statistical mechanics of the liquid-gas surface model fluids in the mean-field approximation computer simulation of the calculation of the density profile three-phase equilibrium interfaces near critical points as mentioned in this paper.
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Diffuse-interface methods in fluid mechanics
TL;DR: Issues including sharp-interface analyses that relate these models to the classical free-boundary problem, computational approaches to describe interfacial phenomena, and models of fully miscible fluids are addressed.
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A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits
TL;DR: In this paper, a variational framework for rate-independent diffusive fracture was proposed based on the introduction of a local history field, which contains a maximum reference energy obtained in the deformation history, which may be considered as a measure for the maximum tensile strain obtained in history.
Journal ArticleDOI
Atomic View of Surface Self‐Diffusion: Tungsten on Tungsten
Gert Ehrlich,F. G. Hudda +1 more
TL;DR: In this paper, the surface diffusion of tungsten adatoms on several smooth, low-index planes of the Tungsten lattice has been followed by direct observation of individual atoms in the field-ion microscope.
Journal ArticleDOI
Step Motion on Crystal Surfaces. II
TL;DR: In this article, it is shown that coalescence of steps or stabilization of step spacings can occur as a consequence of assuming that capture probabilities are directionally dependent, and a general solution for the time-dependent step distribution is obtained in terms of these probabilities and an arbitrary initial distribution of an infinite sequence of parallel steps.