Related papers: Modelling crystallization: When the normal growth …
We estimate density of defects frozen into a biological Turing pattern which was turned on at a finite rate. A self-locking of gene expression in individual cells, which makes the Turing transition discontinuous, stabilizes the pattern…
A variational lattice model is proposed to define an evolution of sets from a single point (nucleation) following a criterion of "maximization" of the perimeter. At a discrete level, the evolution has a "checkerboard" structure and its…
We developed a consistent mathematical model for isotropic crystal growth on a substrate covered by the mask material with a periodic series of parallel long trenches where the substrate is exposed to the vapor phase. Surface diffusion and…
We study the kinetics of the nematic-isotropic transition in a two-dimensional liquid crystal by using a lattice Boltzmann scheme that couples the tensor order parameter and the flow consistently. Unlike in previous studies, we find the…
Our understanding of the growth of crystals is dominated by the classical description according to which individual atoms or molecules, driven by supersaturation, add to crystal facets. As a result, the growth of hard matter is still mostly…
Molecular process of crystallization from an oriented amorphous state was reproduced by molecular dynamics simulation for a realistic polyethylene model. Initial oriented amorphous state was obtained by uniaxial drawing an isotropic glassy…
Colloidal and other granular media experience a transition to rigidity known as jamming if the fill fraction is increased beyond a critical value. The resulting jammed structures are locally disordered, bear applied loads inhomogenously,…
The growth morphology and the effects of surface reconstruction/relaxation of the habit faces on the crystal morphology of urea crystal are investigated from first principle using the Hartman-Perdok approach. A procedure has been developed…
Superficial (two dimensional) crack patterns appear when a thin layer of material elastically attached to a substrate contracts. We study numerically the maturation process undergone by these crack patterns when they are allowed to adapt in…
We consider the scenario where our observable universe is devised as a dynamical four-dimensional hypersurface embedded in a five-dimensional bulk spacetime, with a large extra dimension, which is the {\it generalization of the flat FRW…
We study the dynamics of a growing crystalline facet where the growth mechanism is controlled by the geometry of the local curvature. A continuum model, in (2+1) dimensions, is developed in analogy with the Kardar-Parisi-Zhang (KPZ) model…
Using dynamical density functional theory we calculate the speed of solidification fronts advancing into a quenched two-dimensional model fluid of soft-core particles. We find that solidification fronts can advance via two different…
A region of two-dimensional space has been filled randomly with large number of growing circular discs allowing only a `slight' overlapping among them just before their growth stop. More specifically, each disc grows from a nucleation…
Regularity properties of solutions for a class of quasi-stationary models in one spatial dimension for stress-modulated growth in the presence of a nutrient field are proven. At a given point in time the configuration of a body after pure…
The conditions under which stable evolution of two nonlinear interacting waves are derived within the context of nematic crystals. Two cases are considered: plane waves and solitons. In the first case, the modulation instability analysis…
The crystallization of a binary system is investigated in computer model which takes into account a temperature dependence of diffusion coefficient and a nonequilibrium partition of dissolved component of the alloy. The dependence of…
In this work the effect of amorphous substrate on crystallization is addressed. By performing Monte-Carlo simulations of solid on solid models we explore the effect of the disorder on crystal growth. The disorder is introduced via local…
We examine the molecular dynamics of crystal growth in the presence of surface melting and surface impurities, and from this propose a detailed microscopic model for the growth of ice from the vapor phase. Our model naturally accounts for…
We study numerically the phase-ordering kinetics of the site-diluted and bond-diluted Ising models after a quench from an infinite to a low temperature. We show that the speed of growth of the ordered domain's size is non-monotonous with…
A widely spread method of crystal preparation is to precipitate it from a supersaturated solution. In such a process, control of solution concentration is of paramount importance. Nucleation process, polymorph selection, and crystal habits…