Related papers: Crystal Growth Inside an Octant
The analysis of Coulomb crystallization is extended from one-component to two-component plasmas. Critical parameters for the existence of Coulomb crystals are derived for both classical and quantum crystals. In the latter case, a critical…
We describe laboratory-grown snow crystals that exhibit a triangular, plate-like morphology, and we show that the occurrence of these crystals is much more frequent than one would expect from random growth perturbations of the more-typical…
The growth of crystal surfaces, under non-equilibrium conditions, involves the displacement of mono-atomic steps by atom diffusion and atom incorporations into steps. The time-evolution of the growing crystal surface is thus governed by a…
We investigate strained heteroepitaxial crystal growth in the framework of a simplifying (1+1)-dimensional model by use of off-lattice Kinetic Monte Carlo simulations. Our modified Lennard-Jones system displays the so-called…
Given recipe of qualitative, kinetic modelling by geometric methods of three-dimensional dendritic crystals. Characteristic features of the perturbations appearing on the surface of a spherical body, leading to different scenarios of the…
An effect of the volume change upon proper ferroelastic (martensitic) phase transitions in cubic crystals is considered. Corresponding terms in the Ginzburg-Landau expansion of the Gibbs free energy are analyzed for the first- as well as…
Crystallization, a prototypical self-organization process during which a disordered state spontaneously transforms into a crystal characterized by a regular arrangement of its building blocks, usually proceeds by nucleation and growth. In…
The stability of organic solar cells is strongly affected by the morphology of the photoactive layers, whose separated crystalline and/or amorphous phases are kinetically quenched far from their thermodynamic equilibrium during the…
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…
I show that the evolution of a two dimensional surface in a Laplacian field can be described by Hamiltonian dynamics. First the growing region is mapped conformally to the interior of the unit circle, creating in the process a set of…
The "burst-like growth" regime is observed for the $^4$He crystals with the growth defects. The observation has confirmed the hypothesis for the same physical mechanisms responsible for the transition of the crystalline facets to the state…
We study an effective model of microscopic facet formation for low temperature three dimensional microscopic Wulff crystals above the droplet condensation threshold. The model we consider is a 2+1 solid on solid surface coupled with high…
We describe a novel crystal growth instability that enhances the development of thin edges, promoting the formation of plate-like or hollow columnar morphologies. This instability arises when diffusion-limited growth is coupled with…
Transition metal dichalcogenides exhibit a wide range of semiconducting, metallic, correlated, and topological electronic states that arise from strong coupling between lattice structure, dimensionality, and electronic degrees of freedom.…
A hyperbolic lattice allows for any $p$-fold rotational symmetry, in stark contrast to a two-dimensional crystalline material, where only twofold, threefold, fourfold or sixfold rotational symmetry is permitted. This unique feature…
We study harmonic functions which admit a certain majorant in the unit ball in $\R^m $. We prove that when the majorant fulfills a doubling condition, the extremal growth or decay may occur only along small sets of radii, and we give…
We study complexity in terms of degree growth of one-component lattice equations defined on a $3\times 3$ stencil. The equations include two in Hirota bilinear form and the Boussinesq equations of regular, modified and Schwarzian type.…
We show that solutions of time-dependent degenerate parabolic equations with super-quadratic growth in the gradient variable and possibly unbounded right-hand side are locally ${\mathcal C}^{0,\alpha}$. Unlike the existing (and more…
Here we review a hybrid lattice Boltzmann algorithm to solve the equations of motion of cholesteric liquid crystals. The method consists in coupling a lattice Boltzmann solver for the Navier-Stokes equation to a finite difference method to…
We study the non-equilibrium dynamics of cold atoms held in an optical lattice potential. The expansion of an initially confined atom cloud occurs in two phases: an initial quadratic expansion followed by a ballistic behaviour at long…