We present a real-space, non-periodic, finite-element form ulation for Kohn-Sham Density Functional Theory (KS-DFT). We transform the original vari ational problem into a local saddle-point problem,â€¦ (More)

The vector-valued Allen-Cahn equations are combined with elasticity where a linear stress-strain relationship is assumed. A short physical derivation of the generalised model is given and globalâ€¦ (More)

Using chains of bistable springs, a model is derived to investigate the plastic behavior of carbon nanotube arrays with damage. We study the preconditioning effect due to the loading history byâ€¦ (More)

The tensor-structured methods developed recently for the accurate calculation of the Hartree and the non-local exchange operators have been applied successfully to the ab initio numerical solution ofâ€¦ (More)

For the validity of the weak maximum principle for classical solutions of elliptic partial differential equations it is sufficient that the coefficient matrix a(x) is non-negative. In this note weâ€¦ (More)

Based on a one-dimensional discrete system of bistable springs, a mechanical model is introduced to describe plasticity and damage in carbon nanotube (CNT) arrays. The energetics of the mechanicalâ€¦ (More)

We consider a generalization of the Cahn-Hilliard equation that incorporates an elastic energy density which, being quasi-convex, incorporates micro-structure formation on smaller length scales. Weâ€¦ (More)

We consider a generalisation of the Cahnâ€“Hilliard equation that incorporates an elastic energy density which, being quasiconvex, incorporates microstructure formation on smaller length scales. Weâ€¦ (More)

The Î“-limit of certain discrete free energy functionals related to the numerical approximation of Ginzburg-Landau models is analysed when the distance h between neighbouring points tends to zero. Theâ€¦ (More)