Related papers: Continuum Surface Energy from a Lattice Model
The contribution of the smectic-nematic interface to the surface energy of a nematic liquid crystal sample is analyzed. By means of a simple model it is shown that the surface energy depends on the thickness of the region over which the…
We construct a mathematical model for a diffusiophoretic motion of a deformable droplet, which is floating on a liquid surface and is driven by the surface tension gradient originating from the surface concentration field of the chemicals…
Casimir energy changes are investigated for geometries obtained by small but arbitrary deformations of a given geometry for which the vacuum energy is already known for the massless scalar field. As a specific case, deformation of a…
In this thesis we study energy forms. These are quadratic forms on the space of real-valued measurable $m$-a.e. determined functions $$E:L^0(m) \to [0,\infty],$$ which assign to a measurable function $f$ its energy $E(f)$. Their two…
Classically, surface tension is seen as a force per unit length or as energy per unit area. The surface energy is calculated thermodynamically on the surface of a mathematical layer with no thickness. The surface energy concept is certainly…
We study the effect of boundary rugosity in nematic liquid crystalline systems. We consider a highly general formulation of the problem, able to simultaneously deal with several liquid crystal theories. We use techniques of Gamma…
We study ballistic aggregation on a two dimensional square lattice, where particles move ballistically in between momentum and mass conserving coalescing collisions. Three models are studied based on the shapes of the aggregates: in the…
The relaxation of axisymmetric crystal surfaces with a single facet below the roughening transition is studied via a continuum approach that accounts for step energy g_1 and step-step interaction energy g_3>0. For diffusion-limited…
We propose a method to decompose the total energy of a supercell containing defects into contributions of individual atoms, using the energy density formalism within density functional theory. The spatial energy density is unique up to a…
A continuum density-field formulation with particle-scale resolution is constructed to simultaneously incorporate the orientation dependence of interparticle interactions and the rotational invariance of the system, a fundamental but…
We report an ab initio evaluation of the surface energy of a simple metal, performed via a coupling-constant integration over the dynamical density-response function. The rapid rate of change of the electron density at the surface is…
This paper addresses the problem of consistent energy-based coupling of atomistic and continuum models of materials, limited to zero-temperature statics of simple crystals. It has been widely recognized that the most practical coupled…
We investigate relations between spatial properties of the free energy and the radius of Gaussian curvature of the underlying curved lattice geometries. For this purpose we derive recurrence relations for the analysis of the free energy…
We consider the low-energy particle-particle scattering properties in a periodic simple cubic crystal. In particular, we investigate the relation between the two-body scattering length and the energy shift experienced by the lowest-lying…
We consider the atomistic origin and the main mechanisms determining the energy of a liquid interface after relaxation. A simple theory is constructed for the monatomic densely packed liquids that allows calculation of the surface tension…
We provide a two dimensional deformation model to describe how soft squishy circular particles respond to external forces and collisions. This model involves formulating mathematical equations and algorithms for the shape of a deformed…
A continuum model of crystalline solid equilibrium is presented in which the underlying periodic lattice structure is taken explicitly into account. This model also allows for both point and line defects in the bulk of the lattice and at…
The surface energy is one of the fundamental properties nuclei, appearing in the simplest form of the semi-empirical mass formula. The surface enery has an influence on e.g. the shape of a nucleus and its ability to deform. This in turn…
A continuum field theory approach is presented for modeling elastic and plastic deformation, free surfaces and multiple crystal orientations in non-equilibrium processing phenomena. Many basic properties of the model are calculated…
We study ground-state orderings of particles in classical lattice-gas models of adsorption on crystal surfaces. In the considered models, the energy of adsorbed particles is a sum of two components, each one representing the energy of a…