Related papers: Continuum Surface Energy from a Lattice Model
Energies of a certain class of fullerene molecules (elongated, contracted, and regular icosahedral fullerenes) are numerically calculated using a microscopic description of carbon-carbon bonding. It is shown how these results can be…
In a recent paper by Iglesias, Rumpf and Scherzer (Found. Comput. Math. 18(4), 2018) a variational model for deformations matching a pair of shapes given as level set functions was proposed. Its main feature is the presence of anisotropic…
Some issues that arise when modeling elastic energy for binary alloys are discussed within the context of a Keating model and density functional calculations. The Keating model is based on atomistic modeling of elastic interactions in…
I use the method of classical density-functional theory in the weighted-density approximation of Tarazona to investigate the phase diagram and the interface structure of a two-dimensional lattice-gas model with three phases -- vapour,…
First, we present a two-dimensional lattice gas model with anisotropic interactions which explains the experimentally observed transition from a dominant c(2x2) ordering of the CdTe(001) surface to a local (2x1) arrangement of the Cd atoms…
In the first part of the thesis we consider the constraints of causality and unitarity for particles interacting via strictly finite-range interactions. We generalize Wigner's causality bound to the case of non-vanishing partial-wave…
We present a virtual ionic crystal (VIC) method to calculate energies of charged point defects on surfaces. No artificial charge but an actual zero-dimensional (0D) species is introduced to charge a defect. Effect of dielectric substrate on…
In this continuum theory, we propose a mathematical framework to study the mechanical interplay of bulk-surfaces materials undergoing deformation and phase segregation. To this end, we devise a principle of virtual powers with a…
The advances in cold atom experiments have allowed construction of confining traps in the form of curved surfaces. This opens up the possibility of studying quantum gases in curved manifolds. On closed surfaces, many fundamental processes…
In a finite volume, resonances and multi-hadron states are identified by discrete energy levels. When comparing the results of lattice QCD calculations to scattering experiments, it is important to have a way of associating the energy…
A macroscopic theory for the molecular or Casimir interaction of dielectric materials with arbitrarily shaped surfaces is developed. The interaction is generated by the quantum and thermal fluctuations of the electromagnetic field which…
We study a three-dimensional incompressible viscous fluid in a horizontally periodic domain with finite depth whose free boundary is the graph of a function. The fluid is subject to gravity and generalized forces arising from a surface…
A computational strategy for the evaluation of the crystal lattice constants and cohesive energy of the weakly bound molecular solids is proposed. The strategy is based on the high level ab initio coupled-cluster determination of the…
A new method based on the concept of probability distribution is proposed to analyze the finite volume energy spectrum in lattice QCD. Using synthetic lattice data, we demonstrate that for the channel with quantum numbers of the…
The M\"{o}bius energy is one of the knot energies, and is named after its M\"{o}bius invariant property. It is known to have several different expressions. One is in terms of the cosine of conformal angle, and is called the cosine formula.…
A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane…
We have written expressions for the free energy of a cholesteric liquid crystal in an approximation using the elasticity constants K_1, K_2, K_3 and the energy variation and the corresponding energy and energy gradient along the direction…
The transport of energy in a moving fluid with a simply connected free surface is analyzed, taking into account the contribution of surface tension. This is done by following a "control volume" with arbitrary, specified velocity,…
Molecular crystals play a central role in a wide range of scientific fields, including pharmaceuticals and organic semiconductor devices. However, they are challenging systems to model accurately with computational approaches because of a…
Phase-field models are a leading approach for realistic fracture problems. They treat the crack as a second phase and use gradient terms to smear out the crack faces, enabling the use of standard numerical methods for simulations. This…