A new phase-field model for strongly anisotropic systems
From MaRDI portal
Publication:3561908
DOI10.1098/rspa.2008.0385zbMath1186.80014OpenAlexW2137014774MaRDI QIDQ3561908
Solmaz Torabi, Steven M. Wise, Axel Voigt, John S. Lowengrub
Publication date: 19 May 2010
Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)
Full work available at URL: http://rspa.royalsocietypublishing.org/content/vol465/issue2105/
thin filmCahn-Hilliard equationsquantum dotsphase fieldinterfacial anisotropywillmore regularization
Crystalline structure (74E15) Stefan problems, phase changes, etc. (80A22) Thin films (74K35) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55) Quantum dots, waveguides, ratchets, etc. (81Q37)
Related Items
A Symmetrized Parametric Finite Element Method for Anisotropic Surface Diffusion of Closed Curves ⋮ A perimeter-decreasing and area-conserving algorithm for surface diffusion flow of curves ⋮ Linear second order in time energy stable schemes for hydrodynamic models of binary mixtures based on a spatially pseudospectral approximation ⋮ A note on a phase-field model for anisotropic systems ⋮ Optimal control of anisotropic Allen-Cahn equations ⋮ Existence of solutions for anisotropic Cahn-Hilliard and Allen-Cahn systems in higher space dimensions ⋮ On an anisotropic Allen-Cahn system ⋮ Sixth-order Cahn–Hilliard equations with singular nonlinear terms ⋮ A $\theta$-$L$ Approach for Solving Solid-State Dewetting Problems ⋮ Fast, provably unconditionally energy stable, and second-order accurate algorithms for the anisotropic Cahn-Hilliard model ⋮ Crack kinking in a variational phase-field model of brittle fracture with strongly anisotropic surface energy ⋮ Higher-order anisotropic models in phase separation ⋮ Optimal control of a quasilinear parabolic equation and its time discretization ⋮ Efficient and linear schemes for anisotropic Cahn-Hilliard model using the stabilized-invariant energy quadratization (S-IEQ) approach ⋮ Phase-field modeling and simulation of fracture in brittle materials with strongly anisotropic surface energy ⋮ Accurate and efficient algorithms with unconditional energy stability for the time fractional Cahn–Hilliard and Allen–Cahn equations ⋮ A detailed investigation of the model influencing parameters of the phase‐field fracture approach ⋮ High order accurate and convergent numerical scheme for the strongly anisotropic Cahn–Hilliard model ⋮ The fast scalar auxiliary variable approach with unconditional energy stability for nonlocal Cahn–Hilliard equation ⋮ A parametric finite element method for solid-state dewetting problems with anisotropic surface energies ⋮ A uniquely solvable, positivity-preserving and unconditionally energy stable numerical scheme for the functionalized Cahn-Hilliard equation with logarithmic potential ⋮ Stable Equilibria of Anisotropic Particles on Substrates: A Generalized Winterbottom Construction ⋮ Modeling of brittle fracture in thick plates subjected to transient dynamic loads using a hybrid phase field model ⋮ A diffuse-interface approach for solid-state dewetting with anisotropic surface energies ⋮ The anisotropic Cahn-Hilliard equation: regularity theory and strict separation properties ⋮ Global-in-time Gevrey regularity solutions for the functionalized Cahn-Hilliard equation ⋮ Asymptotic behavior of a sixth-order Cahn-Hilliard system ⋮ Higher-Order Allen–Cahn Models with Logarithmic Nonlinear Terms ⋮ Efficient spectral-Galerkin methods for systems of coupled second-order equations and their applications ⋮ A sixth-order phase-field equation with degenerate mobility ⋮ On a Class of Sixth-Order Cahn--Hilliard-Type Equations with Logarithmic Potential ⋮ Tumor growth and calcification in evolving microenvironmental geometries ⋮ Microstructural patterns with tunable mechanical anisotropy obtained by simulating anisotropic spinodal decomposition ⋮ A second order fully-discrete linear energy stable scheme for a binary compressible viscous fluid model ⋮ A weakly nonlinear, energy stable scheme for the strongly anisotropic Cahn-Hilliard equation and its convergence analysis ⋮ Codimension one minimizers of highly amphiphilic mixtures ⋮ Phase field approach for simulating failure of viscoelastic elastomers ⋮ Unconditionally energy stable second-order numerical schemes for the functionalized Cahn-Hilliard gradient flow equation based on the SAV approach ⋮ Tumor growth in complex, evolving microenvironmental geometries: a diffuse domain approach ⋮ Existence of solutions for two types of generalized versions of the Cahn-Hilliard equation. ⋮ An energy stable algorithm for a quasi-incompressible hydrodynamic phase-field model of viscous fluid mixtures with variable densities and viscosities ⋮ An anisotropic phase-field model based on the equivalent crack surface energy density at finite strain ⋮ Data-driven topology optimization of spinodoid metamaterials with seamlessly tunable anisotropy ⋮ On the viscous Allen-Cahn and Cahn-Hilliard systems with Willmore regularization. ⋮ Higher-order Cahn-Hilliard equations with dynamic boundary conditions ⋮ A Flux-Corrected Phase-Field Method for Surface Diffusion ⋮ Stabilized Predictor-Corrector Schemes for Gradient Flows with Strong Anisotropic Free Energy ⋮ A Finite Element Method for a Phase Field Model of Nematic Liquid Crystal Droplets ⋮ A regularized phase-field model for faceting in a kinetically controlled crystal growth ⋮ The influence of electric fields on nanostructures-simulation and control ⋮ Highly accurate, linear, and unconditionally energy stable large time-stepping schemes for the functionalized Cahn-Hilliard gradient flow equation ⋮ Analysis of the energy stability for stabilized semi-implicit schemes of the functionalized Cahn-Hilliard mass-conserving gradient flow equation ⋮ Efficient energy stable schemes for isotropic and strongly anisotropic Cahn-Hilliard systems with the Willmore regularization ⋮ Sharp-Interface Limits of the Cahn--Hilliard Equation with Degenerate Mobility ⋮ A uniquely solvable, energy stable numerical scheme for the functionalized Cahn-Hilliard equation and its convergence analysis ⋮ Stabilized semi-implicit spectral deferred correction methods for Allen-Cahn and Cahn-Hilliard equations ⋮ A qualitative analysis of a nonlinear second-order anisotropic diffusion problem with non-homogeneous Cauchy-Stefan-Boltzmann boundary conditions ⋮ Robust family of exponential attractors for isotropic crystal models ⋮ Weak solutions for a sixth-order phase-field equation with degenerate mobility ⋮ On nonnegative solutions for the functionalized Cahn-Hilliard equation with degenerate mobility ⋮ Efficient, non-iterative, and second-order accurate numerical algorithms for the anisotropic Allen-Cahn equation with precise nonlocal mass conservation ⋮ The IEQ and SAV approaches and their extensions for a class of highly nonlinear gradient flow systems ⋮ Sixth-order Cahn-Hilliard systems with dynamic boundary conditions ⋮ Fully-discrete spectral-Galerkin numerical scheme with second-order time accuracy and unconditional energy stability for the anisotropic Cahn-Hilliard model ⋮ Well-posedness of a hydrodynamic phase-field system for functionalized membrane-fluid interaction ⋮ The Cahn-Hilliard equation and some of its variants ⋮ How Do Degenerate Mobilities Determine Singularity Formation in Cahn--Hilliard Equations? ⋮ The conforming virtual element method for polyharmonic and elastodynamics problems: a review ⋮ Convex Splitting Method for Strongly Anisotropic Solid-State Dewetting Problems in Two Dimensions ⋮ Spectra of functionalized operators arising from hypersurfaces ⋮ On the phase-field-crystal model with logarithmic nonlinear terms ⋮ Global regular solvability of a nonuniformly nonlinear sixth order Cahn–Hilliard system
Cites Work
