Design of lattice surface energies

The bulk, surface and corner free energies of the square lattice Ising model

We use Kaufman’s spinor method to calculate the bulk, surface and corner free energies ¢ f f f f , , , b s s c of the anisotropic square lattice zero-field Ising model for the ordered ferromagnetic case. For ¢ f f f , , b s s our results of course agree with the early work of Onsager, McCoy and Wu. We also find agreement with the conjectures made by Vernier and Jacobsen (VJ) for the isotropic c...

Optimal Design of a Microgrid with Multiple Energies Considering Reliability

The unprecedented penetration of distributed generation in distribution network provides utilities with a unique opportunity to manage portions of networks as microgrids (MG). The implementation of an MG may offer many benefits, such as capital investments deferral, reduction of greenhouse gas emissions, improvement in reliability, and reduction in network losses. In order to draw the most effe...

Lower semicontinuity of surface energies

Surface energies of elemental crystals

The surface energy is a fundamental property of the different facets of a crystal that is crucial to the understanding of various phenomena like surface segregation, roughening, catalytic activity, and the crystal's equilibrium shape. Such surface phenomena are especially important at the nanoscale, where the large surface area to volume ratios lead to properties that are significantly differen...

Eigenmodes of Surface Energies for Shape Analysis

In this work, we study the spectra and eigenmodes of the Hessian of various discrete surface energies and discuss applications to shape analysis. In particular, we consider a physical model that describes the vibration modes and frequencies of a surface through the eigenfunctions and eigenvalues of the Hessian of a deformation energy, and we derive a closed form representation for the Hessian (...