In this manuscript, singularly perturbed energies with 2, 3, or 4 preferred gradients subject to
incompatible Dirichlet boundary conditions are studied. This extends results on models for …

A new phase-field approach is designed to model surface diffusion of crystals with strongly
anisotropic surface energy. The model can be shown to asymptotically converge toward the …

Taking the well-understood Cu-Ni {111} semi-coherent interface as a prototype, we
demonstrate an important, yet long-been-overlooked, size effect on the properties of …

Phase-field models for strongly anisotropic surface energy need to be regularized to remove
the ill posedness of the dynamic equations. Regularization introduces a new length scale …

At equilibrium, the shape of a strongly anisotropic crystal exhibits corners when for some
orientations the surface stiffness is negative. In the sharp-interface problem, the surface free …

The kinetic equation for anisotropic motion-by-curvature is ill posed when the surface energy
is strongly anisotropic. In this case, corners or edges are present on the Wulff shape, which …

The thermodynamics of strongly anisotropic crystalline surfaces is analogous to that of a
binary mixture exhibiting phase separation. On a metastable planar surface, formation of …

A major current focus in nanotechnology is the precise control of the self-assembling of
semiconductor structures at the nanometric level. Highly uniform structures such as quantum …

We present a covariant theory for the ageing characteristics of phase-ordering systems that
possess dynamical symmetries beyond mere scalings. A chiral spin dynamics which …

Fatigue as the most frequent mode of failure among mechanical systems has been the focus
of a large part of the research community. Modern manufacturing technologies are …