Stable equilibrium configurations of elastic crystals

Equilibrium configurations of defective crystals

Uniqueness of Equilibrium Configurations in Solid Crystals

In this article, under suitable assumptions, it is proved that infu∈UΛ E[u] is dual to sup(a,b){ ∫ Ω a(F(x))dx + ∫ Λ b(y)dy}, where, E[u] := ∫ Ω(h(detDu) − F · u)dx. Here, the infimum is performed over UΛ, the set of all orientation-preserving deformations u ∈ C1(Ω)d that are homeomorphisms from Ω̄ onto Λ̄, and the supremum is performed over the set of all upper semicontinuous functions a, b such...

On equilibrium configurations of nematic liquid crystals droplet with anisotropic elastic energy

We investigate the effect of anisotropic elastic energy on defect patterns of liquid crystals confined in a three-dimensional spherical domain within the framework of Landau–de Gennes model. Two typical strong anchoring boundary conditions, namely homeotropic and mirror-homeotropic anchoring conditions, are considered. For the homeotropic anchoring, we find three different configurations: uniax...

Equilibrium form of crystals and stable norm

The equilibrium form of a crystal is the shape which minimizes the total surface tension for a given volume. The surface tension itself is considered to be a function of the orientation of the crystal face within the crystal lattice. This function of orientation is identified with the stable norm on the second homology classes of a Riemannian 3-torus. Minimizing the total surface tension of the...

Regularity Properties of Equilibrium Configurations of Epitaxially Strained Elastic Films

We consider a variational model introduced in the physical literature to describe the epitaxial growth of an elastic film over a rigid substrate, when a lattice mismatch between the two materials is present. We establish the regularity of volume constrained local minimizers of the total energy, proving in particular the so called zero contact-angle condition between the film and the substrate.