Numerical Approximation of the Two-Component PFC Models for Binary Colloidal Crystals: Efficient, Decoupled, and Second-Order Unconditionally Energy Stable Schemes

Efficient, decoupled, and second-order unconditionally energy stable numerical schemes for the coupled Cahn–Hilliard system in copolymer/homopolymer mixtures

(2020) Qi Li et al.   COMPUTER PHYSICS COMMUNICATIONS

A new Lagrange multiplier approach for gradient flows

(2020) Qing Cheng et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Highly efficient and linear numerical schemes with unconditional energy stability for the anisotropic phase-field crystal model

(2020) Qi Li et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Efficient numerical schemes with unconditional energy stabilities for the modified phase field crystal equation

(2019) Qi Li et al.   ADVANCES IN COMPUTATIONAL MATHEMATICS

Numerical approximations for a new L2-gradient flow based Phase field crystal model with precise nonlocal mass conservation

(2019) Jun Zhang et al.   COMPUTER PHYSICS COMMUNICATIONS

On efficient numerical schemes for a two-mode phase field crystal model with face-centered-cubic (FCC) ordering structure

(2019) Jun Zhang et al.   APPLIED NUMERICAL MATHEMATICS

Phase ordering, transformation, and grain growth of two-dimensional binary colloidal crystals: A phase field crystal modeling

(2019) Doaa Taha et al.   Physical Review Materials

Stability of three-dimensional icosahedral quasicrystals in multi-component systems

(2019) Kai Jiang et al.   PHILOSOPHICAL MAGAZINE

The scalar auxiliary variable (SAV) approach for gradient flows

(2018) Jie Shen et al.   JOURNAL OF COMPUTATIONAL PHYSICS

The meshless local collocation method for solving multi-dimensional Cahn-Hilliard, Swift-Hohenberg and phase field crystal equations

(2017) Mehdi Dehghan et al.   ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS

Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model

(2017) Xiaofeng Yang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Grain Boundary Structures and Collective Dynamics of Inversion Domains in Binary Two-Dimensional Materials

(2017) Doaa Taha et al.   PHYSICAL REVIEW LETTERS

Colloidal molecules assembled from binary spheres under an AC electric field

(2017) Kelley Lynch Heatley et al.   Soft Matter

Stability of Soft Quasicrystals in a Coupled-Mode Swift-Hohenberg Model for Three-Component Systems

(2016) Kai Jiang et al.   Communications in Computational Physics

A binary phase field crystal study for phase segregation of liquid phase heteroepitaxial growth

(2016) Yingying Peng et al.   COMPUTATIONAL MATERIALS SCIENCE

First and second order numerical methods based on a new convex splitting for phase-field crystal equation

(2016) Jaemin Shin et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Improving the accuracy of convexity splitting methods for gradient flow equations

(2016) Karl Glasner et al.   JOURNAL OF COMPUTATIONAL PHYSICS

On Second Order Semi-implicit Fourier Spectral Methods for 2D Cahn–Hilliard Equations

(2016) Dong Li et al.   JOURNAL OF SCIENTIFIC COMPUTING

Local Discontinuous Galerkin Method and High Order Semi-Implicit Scheme for the Phase Field Crystal Equation

(2016) Ruihan Guo et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

First and second order operator splitting methods for the phase field crystal equation

(2015) Hyun Geun Lee et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Phase transformations in binary colloidal monolayers

(2015) Ye Yang et al.   Soft Matter

Self-assembled binary colloidal crystal monolayers as cell culture substrates

(2015) Peng-Yuan Wang et al.   Journal of Materials Chemistry B

Fabrication of Well-Ordered Binary Colloidal Crystals with Extended Size Ratios for Broadband Reflectance

(2014) Zhongyu Cai et al.   ACS Applied Materials & Interfaces

Characterizing solute segregation and grain boundary energy in binary alloy phase field crystal models

(2013) Jonathan Stolle et al.   COMPUTATIONAL MATERIALS SCIENCE

Colloidal particles in a drying suspension: A phase field crystal approach

(2013) Nirmalendu Ganai et al.   EUROPEAN PHYSICAL JOURNAL E

Energy stable and efficient finite-difference nonlinear multigrid schemes for the modified phase field crystal equation

(2013) Arvind Baskaran et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Convergence Analysis of a Second Order Convex Splitting Scheme for the Modified Phase Field Crystal Equation

(2013) A. Baskaran et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

An unconditionally energy-stable method for the phase field crystal equation

(2012) Hector Gomez et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Electrostatic assembly of binary nanoparticle superlattices using protein cages

(2012) Mauri A. Kostiainen et al.   Nature Nanotechnology

Phase-field crystal modeling of early stage clustering and precipitation in metal alloys

(2012) Vahid Fallah et al.   PHYSICAL REVIEW B

Binary colloidal structures assembled through Ising interactions

(2012) Karim S. Khalil et al.   Nature Communications

An Energy Stable and Convergent Finite-Difference Scheme for the Modified Phase Field Crystal Equation

(2011) C. Wang et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Numerical approximations of Allen-Cahn and Cahn-Hilliard equations

(2010) Jie Shen et al.   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

Energetic and Entropic Contributions to Self-Assembly of Binary Nanocrystal Superlattices: Temperature as the Structure-Directing Factor

(2010) Maryna I. Bodnarchuk et al.   JOURNAL OF THE AMERICAN CHEMICAL SOCIETY

Entropy-Driven Formation of Binary Semiconductor-Nanocrystal Superlattices

(2010) Wiel H. Evers et al.   NANO LETTERS

Morphological instability, evolution, and scaling in strained epitaxial films: An amplitude-equation analysis of the phase-field-crystal model

(2010) Zhi-Feng Huang et al.   PHYSICAL REVIEW B

Phase-field-crystal dynamics for binary systems: Derivation from dynamical density functional theory, amplitude equation formalism, and applications to alloy heterostructures

(2010) Zhi-Feng Huang et al.   PHYSICAL REVIEW E

Tuning the structure of non-equilibrium soft materials by varying the thermodynamic driving force for crystal ordering

(2010) György Tegze et al.   Soft Matter

Design of 2D Binary Colloidal Crystals in a Nematic Liquid Crystal

(2009) U. Ognysta et al.   LANGMUIR

Simulation and fabrication of binary colloidal photonic crystals and their inverse structures

(2009) Yong Wan et al.   MATERIALS LETTERS

Magnetic 3-D ordered macroporous silica templated from binary colloidal crystals and its application for effective removal of microcystin

(2009) Jia Liu et al.   MICROPOROUS AND MESOPOROUS MATERIALS

Derivation of the phase-field-crystal model for colloidal solidification

(2009) Sven van Teeffelen et al.   PHYSICAL REVIEW E

Advanced operator splitting-based semi-implicit spectral method to solve the binary phase-field crystal equations with variable coefficients

(2008) György Tegze et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Mesoscopic and Microscopic Modeling of Island Formation in Strained Film Epitaxy

(2008) Zhi-Feng Huang et al.   PHYSICAL REVIEW LETTERS