Related papers: Equilibrium Shape of Crystals
Macroscopic models of nucleation provide powerful tools for understanding activated phase transition processes. These models do not provide atomistic insights and can thus sometime lack material-specific descriptions. Here we provide a…
We consider the shape of crystals which are soft in the sense that their elastic modulus $\mu$ is small compared to their surface tension $\gamma$, more precisely $ \mu a < \gamma$ where $a$ is the lattice spacing. We show that their…
Alternative approach for description of the non-equilibrium phenomena arising in solids at a severe external loading is analyzed. The approach is based on the new form of kinetic equations in terms of the internal and modified free energy.…
The purpose of the study is to further investigate the classical Gibbs analysis of the heterogeneous system "stressed crystal - melt." It is demonstrated that each equilibrium configuration is stable with respect to a special class of…
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…
The crystallization of electrons in quasi low-dimensional solids is studied in a model which retains the full three-dimensional nature of the Coulomb interactions. We show that restricting the electron motion to layers (or chains) gives…
Computing equilibrium shapes of crystals (ESC) is a challenging problem in materials science that involves minimizing an orientation-dependent (i.e., anisotropic) surface energy functional subject to a prescribed mass constraint. The highly…
A phase eld approach is developed to model wetting and heterogeneous crystal nucleation of an undercooled pure liquid in contact with a sharp wall. We discuss various choices for the boundary condition at the wall and determine the…
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…
Quantum theory is proposed of high energy electrons scattering in ultrathin crystals. This theory is based upon a special representation of the scattering amplitude in the form of the integral over the surface surrounding the crystal, and…
The nonequilibrium phase transition in a system of diffusing, coagulating particles in the presence of a steady input and evaporation of particles is studied. The system undergoes a transition from a phase in which the average number of…
We investigate a theoretical framework for modeling fluid turbulence based on the formalism of exact coherent structures (ECSs). Although highly promising, existing evidence for the role of ECSs in turbulent flows is largely circumstantial…
Given a positive function F on S n satisfying an appropriate con-vexity assumption, we consider hypersurfaces for which a linear combination of some higher order anisotropic curvatures is constant. We define the varia-tional problem for…
We propose diagrams representing the equilibrium morphologies of two immiscible liquid droplets brought into contact. We study the dependence of the shape of the droplets on the surface tensions and ratio of volumes. We study theoretically…
Deformations of heavy elastic cylinders with their axis in the direction of earth's gravity field are investigated. The specimens, made of polyacrylamide hydrogels, are attached from their top circular cross section to a rigid plate. An…
Let $K$ be a convex polyhedron and $\mathscr F$ its Wulff energy, and let $\mathscr C(K)$ denote the set of convex polyhedra close to $K$ whose faces are parallel to those of $K$. We show that, for sufficiently small $\epsilon$, all…
The initial techniques developed in Euclid's Elements, well before the use of the parallel postulate, are reexamined in order to clarify even the most obscure details, particularly those related to equality, superposition and angle…
We use molecular dynamics simulations to study the melting of gold icosahedral clusters of a few thousand atoms. We pay particular attention to the behavior of surface atoms, and to the equilibrium shape of the cluster. We find that…
A continuum theory is used to predict scaling laws for the morphological relaxation of crystal surfaces in two independent space dimensions. The goal is to unify previously disconnected experimental observations of decaying surface…
We study the formation and growth of equilibrium clusters in a suspension of weakly-charged colloidal particles and small non-adsorbing polymers. The effective potential is characterised by a short-range attraction and a long-range…