A convergent convex splitting scheme for the periodic nonlocal Cahn-Hilliard equation

[1]  Cheng Wang,et al.  Second order convex splitting schemes for periodic nonlocal Cahn-Hilliard and Allen-Cahn equations , 2014, J. Comput. Phys..

[2]  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 .

[3]  Kun Zhou,et al.  Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints , 2012, SIAM Rev..

[4]  Cheng Wang,et al.  Energy stable and efficient finite-difference nonlinear multigrid schemes for the modified phase field crystal equation , 2012, J. Comput. Phys..

[5]  H. Löwen,et al.  Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview , 2012, 1207.0257.

[6]  Ioannis G Kevrekidis,et al.  Dynamic density functional theory of solid tumor growth: Preliminary models. , 2012, AIP advances.

[7]  Nasser Mohieddin Abukhdeir,et al.  Long-time integration methods for mesoscopic models of pattern-forming systems , 2011, J. Comput. Phys..

[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]  Kun Zhou,et al.  Mathematical and Numerical Analysis of Linear Peridynamic Models with Nonlocal Boundary Conditions , 2010, SIAM J. Numer. Anal..

[10]  S. M. Wise,et al.  Unconditionally Stable Finite Difference, Nonlinear Multigrid Simulation of the Cahn-Hilliard-Hele-Shaw System of Equations , 2010, J. Sci. Comput..

[11]  Steven M. Wise,et al.  Unconditionally stable schemes for equations of thin film epitaxy , 2010 .

[12]  Cheng Wang,et al.  Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation , 2009, J. Comput. Phys..

[13]  Thomas Wanner,et al.  A semi-implicit spectral method for stochastic nonlocal phase-field models , 2009 .

[14]  Cheng Wang,et al.  An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation , 2009, SIAM J. Numer. Anal..

[15]  Ekkehard W. Sachs,et al.  Efficient solution of a partial integro-differential equation in finance , 2008 .

[16]  H. Frieboes,et al.  Three-dimensional multispecies nonlinear tumor growth--I Model and numerical method. , 2008, Journal of theoretical biology.

[17]  E. Favvas,et al.  What is spinodal decomposition , 2008 .

[18]  Hartmut Löwen,et al.  Colloidal crystal growth at externally imposed nucleation clusters. , 2008, Physical review letters.

[19]  Gerhard Kahl,et al.  Why do ultrasoft repulsive particles cluster and crystallize? Analytical results from density-functional theory. , 2007, The Journal of chemical physics.

[20]  Peter W. Bates,et al.  On a nonlocal phase-field system , 2006 .

[21]  Peter W. Bates,et al.  The Dirichlet boundary problem for a nonlocal Cahn–Hilliard equation , 2005 .

[22]  Klaus Gärtner,et al.  On a nonlocal model of image segmentation , 2005 .

[23]  Peter W. Bates,et al.  The Neumann boundary problem for a nonlocal Cahn–Hilliard equation , 2005 .

[24]  A. Archer,et al.  Dynamical density functional theory and its application to spinodal decomposition. , 2004, The Journal of chemical physics.

[25]  Andrew J. Archer,et al.  Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic? , 2004, cond-mat/0405603.

[26]  Herbert Gajewski,et al.  On a nonlocal phase separation model , 2003 .

[27]  J. Dzubiella,et al.  Mean-field dynamical density functional theory , 2003, cond-mat/0301345.

[28]  Markos A. Katsoulakis,et al.  Spectral methods for mesoscopic models of pattern formation , 2001 .

[29]  Martin Grant,et al.  Modeling elasticity in crystal growth. , 2001, Physical review letters.

[30]  Jeffrey W. Bullard,et al.  Computational and mathematical models of microstructural evolution , 1998 .

[31]  P. Tarazona,et al.  Dynamic density functional theory of fluids , 1998, cond-mat/9810403.

[32]  Joel Lebowitz,et al.  Phase Segregation Dynamics in Particle Systems with Long Range Interactions II: Interface Motion , 1997, SIAM J. Appl. Math..

[33]  Giambattista Giacomin,et al.  Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limits , 1997, comp-gas/9705001.

[34]  Enza Orlandi,et al.  Glauber evolution with Kac potentials. I. Mesoscopic and macroscopic limits, interface dynamics , 1994 .

[35]  R. Evans.  The nature of the liquid-vapour interface and other topics in the statistical mechanics of non-uniform, classical fluids , 1979 .

[36]  J. E. Hilliard,et al.  Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .

[37]  Jie Shen,et al.  Second-order Convex Splitting Schemes for Gradient Flows with Ehrlich-Schwoebel Type Energy: Application to Thin Film Epitaxy , 2012, SIAM J. Numer. Anal..

[38]  P. Bates,et al.  International Journal of C 2009 Institute for Scientific Numerical Analysis and Modeling Computing and Information Numerical Analysis for a Nonlocal Allen-cahn Equation , 2022 .

[39]  Xinfu Chen,et al.  ON SOME NONLOCAL EVOLUTION EQUATIONS ARISING IN MATERIALS SCIENCE , 2008 .

[40]  Mihai Anitescu,et al.  IMPLICIT FOR LOCAL EFFECTS AND EXPLICIT FOR NONLOCAL EFFECTS IS UNCONDITIONALLY STABLE , 2004 .

[41]  Paul C. Fife,et al.  Some Nonclassical Trends in Parabolic and Parabolic-like Evolutions , 2003 .

[42]  D. J. Eyre.  Unconditionally Gradient Stable Time Marching the Cahn-Hilliard Equation , 1998 .

[43]  Enza Orlandi,et al.  Uniqueness of the instanton profile and globalstability in non local evolution equations , 1994 .

[44]  R. Temam,et al.  Navier-Stokes equations: theory and numerical analysis: R. Teman North-Holland, Amsterdam and New York. 1977. 454 pp. US $45.00 , 1978 .