By measuring the geometry and crystallography of the three interfaces that meet at grain boundary thermal grooves, it is possible to determine the anisotropy of the surface free energy. Previously, the surface energy of MgO at 1400◦C in air was approximated by a truncated double Fourier series with coefficients that were determined by fitting the observations to Herring’s condition for local eq...

Lattice-model calculations of the energies of surface director-configurations are presented. These configurations mediate between the homeotropic surface conditions and the bulk fingerprint texture of cholesteric layers. Their energy determines the asymptotic behaviour of the cholesteric-nematic threshold field in the limit of thick layers. The dependence of their energies on the elastic consta...

Surface energies and relaxations are calculated within the tight-binding formalism and including also repulsive interatomic interactions. At fcc and bcc metal surfaces we obtain damped oscillatory multilayer relaxations. Furthermore, we present results for the reconstruction at clean (110) and (100) surfaces of Ir, Pt and Au. CO-suppressed and H-induced reconstruction observed at some transitio...

We consider weakly convergent sequences of approximate H-surface maps defined in the plane with their tension fields bounded in Lp for p > 4/3, and establish an energy quantization that accounts for the loss of their energies by the sum of energies over finitely many nontrivial bubbles maps on R2. As a direct consequence, we establish the energy identity at finite singular time to their H-surfa...

We construct a generalized gradient approximation of the exchange-correlation energy that satisfies the nonuniform scaling in one dimension and is accurate in the whole quasi-two-dimensional (Q2D) regime. Using spatial and energetic analyses of metal (111) surfaces, we show that the Q2D behavior is important at the surface of most transition metals, and that the here proposed Q2D-generalized gr...

We show how some problems coming from different fields of applied sciences such as physics, engineering, biology, admit a common variational formulation characterized by the competition of two energetic terms. We discuss related problems and techniques studied by the authors and collaborators in the recent past as well open problems and further possible research directions in these topics.

We study the stability of surfaces trapped between two parallel planes with free boundary on these planes. The energy functional consists of anisotropic surface energy, wetting energy, and line tension. Equilibrium surfaces are surfaces with constant anisotropic mean curvature. We study the case where the Wulff shape is of a special type of “product form”, that is, its horizontal sections are a...

We study the stability of closed, not necessarily smooth, equilibrium surfaces of an anisotropic surface energy for which the Wulff shape is not necessarily smooth. We show that if the Cahn Hoffman field can be extended continuously to the whole surface and if the surface is stable, then the surface is, up to rescaling, the Wulff shape. 2010 AMS classification: 49Q10

Metallic superlattices with planar, unalloyed (unmixed) interfacial structures are difficult to fabricate by all conventional vapor deposition methods. Molecular dynamics simulations have been used to explore the ways in which inert gas ions can be used to control the atomic assembly of a model Cu/Co metallic super lattice system. High energy, high atomic weight ions are shown to smooth rough i...