Convergence analysis for second-order accurate schemes for the periodic nonlocal Allen-Cahn and Cahn-Hilliard equations

Energy stable multigrid method for local and non-local hydrodynamic models for freezing

(2016) Arvind Baskaran et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Asymptotically Compatible Fourier Spectral Approximations of Nonlocal Allen--Cahn Equations

(2016) Qiang Du et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

A diffuse interface model for two-phase incompressible flows with non-local interactions and non-constant mobility

(2015) Sergio Frigeri et al.   NONLINEARITY

Kinetic density functional theory of freezing

(2014) Arvind Baskaran et al.   JOURNAL OF CHEMICAL PHYSICS

Second order convex splitting schemes for periodic nonlocal Cahn–Hilliard and Allen–Cahn equations

(2014) Zhen Guan et al.   JOURNAL OF COMPUTATIONAL PHYSICS

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

(2014) Zhen Guan et al.   NUMERISCHE MATHEMATIK

Phase field crystal modeling as a unified atomistic approach to defect dynamics

(2014) Joel Berry et al.   PHYSICAL REVIEW B

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

Second-order Convex Splitting Schemes for Gradient Flows with Ehrlich–Schwoebel Type Energy: Application to Thin Film Epitaxy

(2012) Jie Shen et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints

(2012) Qiang Du et al.   SIAM REVIEW

Dynamic density functional theory of solid tumor growth: Preliminary models

(2012) Arnaud Chauviere et al.   AIP Advances

Interface Conditions for a Phase Field Model with Anisotropic and Non-Local Interactions

(2011) Xinfu Chen et al.   ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS

Long-time integration methods for mesoscopic models of pattern-forming systems

(2011) Nasser Mohieddin Abukhdeir et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Global existence of weak solutions to a nonlocal Cahn–Hilliard–Navier–Stokes system

(2011) Pierluigi Colli et al.   JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

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

Unconditionally stable schemes for equations of thin film epitaxy

(2010) Steven Wise et al.   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

Unconditionally Stable Finite Difference, Nonlinear Multigrid Simulation of the Cahn-Hilliard-Hele-Shaw System of Equations

(2010) S. M. Wise   JOURNAL OF SCIENTIFIC COMPUTING

Three-dimensional multispecies nonlinear tumor growth—II: Tumor invasion and angiogenesis

(2010) Hermann B. Frieboes et al.   JOURNAL OF THEORETICAL BIOLOGY

Free Energy Functionals for Efficient Phase Field Crystal Modeling of Structural Phase Transformations

(2010) Michael Greenwood et al.   PHYSICAL REVIEW LETTERS

Mathematical and Numerical Analysis of Linear Peridynamic Models with Nonlocal Boundary Conditions

(2010) Kun Zhou et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

A semi-implicit spectral method for stochastic nonlocal phase-field models

(2009) Tina Hartley et al.   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation

(2009) Z. Hu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

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

(2009) S. M. Wise et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Adding Adhesion to a Chemical Signaling Model for Somite Formation

(2008) Nicola J. Armstrong et al.   BULLETIN OF MATHEMATICAL BIOLOGY

Three-dimensional multispecies nonlinear tumor growth—I

(2008) S.M. Wise et al.   JOURNAL OF THEORETICAL BIOLOGY

Efficient solution of a partial integro-differential equation in finance

(2007) E.W. Sachs et al.   APPLIED NUMERICAL MATHEMATICS

Mathematical modelling of cancer cell invasion of tissue: Local and non-local models and the effect of adhesion

(2007) A. Gerisch et al.   JOURNAL OF THEORETICAL BIOLOGY