Higher-order anisotropic models in phase separation
暂无分享,去创建一个
[1] Peter Galenko,et al. Phase-field-crystal and Swift-Hohenberg equations with fast dynamics. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.
[2] Hao Wu,et al. Robust exponential attractors for the modified phase-field crystal equation , 2013 .
[3] Axel Voigt,et al. A new phase-field model for strongly anisotropic systems , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[4] Alain Miranville,et al. Sixth‐order Cahn–Hilliard systems with dynamic boundary conditions , 2015 .
[5] S. Agmon,et al. Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I , 1959 .
[6] Steven M. Wise,et al. Global Smooth Solutions of the Three-dimensional Modified Phase Field Crystal Equation , 2010 .
[7] Gompper,et al. Ginzburg-Landau theory of ternary amphiphilic systems. I. Gaussian interface fluctuations. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.
[8] Steven M. Wise,et al. An Energy Stable and Convergent Finite-Difference Scheme for the Modified Phase Field Crystal Equation , 2011, SIAM J. Numer. Anal..
[9] S. Agmon. Lectures on Elliptic Boundary Value Problems , 1965 .
[10] Cheng Wang,et al. An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation , 2009, SIAM J. Numer. Anal..
[11] Alain Miranville,et al. Sixth-order Cahn–Hilliard equations with singular nonlinear terms , 2015 .
[12] Piotr Rybka,et al. On a Higher Order Convective Cahn-Hilliard-Type Equation , 2012, SIAM J. Appl. Math..
[13] Jie Shen,et al. Efficient energy stable schemes with spectral discretization in space for anisotropic , 2013 .
[14] J. E. Hilliard,et al. Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .
[15] John W. Cahn,et al. On Spinodal Decomposition , 1961 .
[16] Alain Miranville,et al. Higher-Order Allen–Cahn Models with Logarithmic Nonlinear Terms , 2016 .
[17] Piotr Rybka,et al. Global Weak Solutions to a Sixth Order Cahn-Hilliard Type Equation , 2012, SIAM J. Math. Anal..
[18] P. Voorhees,et al. Faceting of a growing crystal surface by surface diffusion. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.
[19] A. Miranville,et al. Higher-order models in phase separation , 2016 .
[20] Joel Lebowitz,et al. Phase Segregation Dynamics in Particle Systems with Long Range Interactions II: Interface Motion , 1997, SIAM J. Appl. Math..
[21] Alain Miranville,et al. On the phase-field-crystal model with logarithmic nonlinear terms , 2016 .
[22] Gunduz Caginalp,et al. Anisotropic phase field equations of arbitrary order , 2010 .
[23] Amy Novick-Cohen,et al. Chapter 4 The Cahn–Hilliard Equation , 2008 .
[24] Gunduz Caginalp,et al. Interface Conditions for a Phase Field Model with Anisotropic and Non-Local Interactions , 2011 .
[25] J. Taylor,et al. II—mean curvature and weighted mean curvature , 1992 .
[26] Sergey Zelik,et al. The Cahn-Hilliard Equation with Logarithmic Potentials , 2011 .
[27] J. E. Hilliard,et al. Free Energy of a Nonuniform System. I. Interfacial Free Energy and Free Energy of a Nonuniform System. III. Nucleation in a Two‐Component Incompressible Fluid , 2013 .
[28] R. Kobayashi. Modeling and numerical simulations of dendritic crystal growth , 1993 .
[29] Gompper,et al. Ginzburg-Landau theory of ternary amphiphilic systems. II. Monte Carlo simulations. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.
[30] Alain Miranville,et al. Asymptotic behavior of a sixth-order Cahn-Hilliard system , 2013 .
[31] P. Gennes. Dynamics of fluctuations and spinodal decomposition in polymer blends , 1980 .
[32] I. Pawlow,et al. On a class of sixth order viscous Cahn-Hilliard type equations , 2012 .
[33] Frédéric Hecht,et al. New development in freefem++ , 2012, J. Num. Math..
[34] Giulio Schimperna,et al. On a Class of Cahn-Hilliard Models with Nonlinear Diffusion , 2011, SIAM J. Math. Anal..
[35] G. B. McFadden,et al. On the notion of a ξ–vector and a stress tensor for a general class of anisotropic diffuse interface models , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.
[36] Sergey Zelik,et al. Chapter 3 Attractors for Dissipative Partial Differential Equations in Bounded and Unbounded Domains , 2008 .
[37] J. Cahn,et al. A microscopic theory for antiphase boundary motion and its application to antiphase domain coasening , 1979 .
[38] G. Gompper. Ginzburg‐Landau Theories of Ternary Amphiphilic Systems , 1996 .
[39] M. Grant,et al. Diffusive atomistic dynamics of edge dislocations in two dimensions. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.
[40] Joel Berry,et al. Simulation of an atomistic dynamic field theory for monatomic liquids: freezing and glass formation. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.
[41] H. Löwen,et al. Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview , 2012, 1207.0257.
[42] Maurizio Grasselli,et al. Well-posedness and longtime behavior for the modified phase-field crystal equation , 2013 .
[43] Cheng Wang,et al. Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation , 2009, J. Comput. Phys..
[44] Richard E. Mortensen,et al. Infinite-Dimensional Dynamical Systems in Mechanics and Physics (Roger Temam) , 1991, SIAM Rev..
[45] I. Pawlow,et al. A Cahn-Hilliard equation with singular diffusion , 2012, 1206.5604.
[46] Irena Pawłow,et al. A sixth order Cahn-Hilliard type equation arising in oil-water-surfactant mixtures , 2011 .