Related papers: Crystal Shapes and Phase Equilibria: A Common Math…
The phase-field-crystal model is used to access the structure and thermodynamics of interfaces between two coexisting liquid crystalline phases in two spatial dimensions. Depending on the model parameters there is a variety of possible…
The phase-field crystal equation, a parabolic, sixth-order and nonlinear partial differential equation, has generated considerable interest as a possible solution to problems arising in molecular dynamics. This is because the phase-field…
This paper introduces a new structural phase field crystal (PFC) type model that expands the PFC methodology to a wider class of structurally complex crystal structures than previously possible. Specifically, our new approach allows for…
We consider a two-dimensional layer of dipolar particles in the regime of strong dipole moments. Here we can describe the system using classical methods and determine the crystal structure that minimizes the total energy. The dipoles are…
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…
Surface energies for different GaAs surface orientations have been calculated as a function of the chemical potential. We use an energy density formalism within the first-principles pseudopotential density-functional approach. The…
Equilibrium polyethylene crystal structure, cohesive energy, and elastic constants are calculated by density-functional theory applied with a recently proposed density functional (vdW-DF) for general geometries [Phys. Rev. Lett. 92, 246401…
The parametric equations of the plane curves determining the equilibrium shapes that a uniform inextensible elastic ring or tube could take subject to a uniform hydrostatic pressure are presented in an explicit analytic form. The…
Liquid crystals with molecules constrained to the tangent bundle of a curved surface show interesting phenomena resulting from the tight coupling of the elastic and bulk free energies of the liquid crystal with geometric properties of the…
The present work revisits the classical Wulff problem restricted to crystalline integrands, a class of surface energies that gives rise to finitely faceted crystals. The general proof of the Wulff theorem was given by J.E. Taylor (1978) by…
We use surface tension to distinguish between phases with isotropic internal structure from phases which are microscopically anisotropic. There are many interesting open problems, especially in two dimensions, and in phase coexistence.
We consider a class of liquid crystal free-boundary problems for which both the equilibrium shape and internal configuration of a system must simultaneously be determined, for example in films with air- or fluid-liquid crystal interfaces…
Directional solidification of water-based solutions has emerged as a versatile technique to template hierarchical porous materials, but this nonequilibrium process remains incompletely understood. Here we use phase-field simulations to shed…
The relative stability of three-dimensional icosahedral quasicrystals in multi-component systems has been investigated based on a coupled-mode Swift-Hohenberg model with two-length-scales. A recently developed projection method, which…
We consider both equilibrium and kinetic aspects of the phase separation (``thermal faceting") of thermodynamically unstable crystal surfaces into a hill--valley structure. The model we study is an Ising lattice gas for a simple cubic…
We use the Dynamic Density-Functional Formalism and the Fundamental Measure Theory as applied to a fluid of parallel hard squares to study the dynamics of heterogeneous growth of non-uniform phases with columnar and crystalline symmetries.…
Morphological instability of the solid-liquid interface occuring in a crystal growing from an undercooled thin liquid being bounded on one side by a free surface and flowing down inclined plane is investigated by a linear stability analysis…
The topology and the geometry of a surface play a fundamental role in determining the equilibrium configurations of thin films of liquid crystals. We propose here a theoretical analysis of a recently introduced surface Frank energy, in the…
We construct a novel approach, based on thermodynamic geometry, to characterize first-order phase transitions from a microscopic perspective, through the scalar curvature in the equilibrium thermodynamic state space. Our method resolves key…
We present a unified variational treatment of evolving configurations in crystalline solids with microstructure. The crux of our treatment lies in the introduction of a vector configurational field. This field lies in the material, or…