Related papers: A Simple Model for Anisotropic Step Growth
The growth of bacterial flagellar filaments is a self-assembly process where flagellin molecules are transported through the narrow core of the flagellum and are added at the distal end. To model this situation, we generalize a growth…
We point out how geometric features affect the scaling properties of non-equilibrium dynamic processes, by a model for surface growth where particles can deposit and evaporate only in dimer form, but dissociate on the surface. Pinning…
We describe a comprehensive model for the formation and morphological development of atmospheric ice crystals growing from water vapor, also known as snow crystals. Our model derives in part from empirical measurements of the intrinsic ice…
Steps with spacings of microns form on top of mesas fabricated on Si(111) that is annealed at temperatures where sublimation becomes important. Upon annealing, mesas first develop ridges along their edges, effectively creating craters which…
We study an initial value problem for two-dimensional needle crystal growth with anisotropic surface tension. The initial value problem is derived from the so called one-sided model based on complex variables method. We then obtain the…
We present a systematic study of the morphology of homoepitaxial InP films grown by metalorganic vapor-phase epitaxy which are imaged with ex situ atomic force microscopy. These films show a dramatic range of different surface morphologies…
A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to times scales…
We model shell formation of core-shell noble metal nanoparticles. A recently developed kinetic Monte Carlo approach is utilized to reproduce growth morphologies realized in recent experiments on core-shell nanoparticle synthesis, which…
We study conserved models of crystal growth in one dimension [$\partial_t z(x,t) =-\partial_x j(x,t)$] which are linearly unstable and develop a mound structure whose typical size L increases in time ($L = t^n$). If the local slope ($m…
We study analytically and numerical the growth rate of a crystal surface growing by several screw dislocations. To describe several spiral steps we use the revised level set method for spirals by the authors (Journal of Scientific Computing…
This work presents new asymptotic formulas for family of walks in Weyl chambers. The models studied here are defined by step sets which exhibit many symmetries and are restricted to the first orthant. The resulting formulas are very…
Growth of hard--rod monolayers via deposition is studied in a lattice model using rods with discrete orientations and in a continuum model with hard spherocylinders. The lattice model is treated with kinetic Monte Carlo simulations and…
Using coherent x-ray scattering, we evidenced atomic step roughness at the [111] vicinal surface of a silicon monocrystal of 0.05 degree miscut. Close to the (1/2 1/2 1/2) anti-Bragg position of the reciprocal space which is particularly…
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…
Immense interests in thin-film fabrication for industrial applications have driven both theoretical and computational aspects of modeling its growth with an aim to design and control film's surface morphology. Oftentimes, smooth surface is…
Modeling the spontaneous evolution of morphology in natural systems and its preservation by proportionate growth remains a major scientific challenge. Yet, it is conceivable that if the basic mechanisms of growth and the coupled kinetic…
Silicon self-assembly at step edges in the initial stage of homoepitaxial growth on a vicinal Si(111) surface is studied by scanning tunneling microscopy (STM). The resulting atomic structures change dramatically from a parallel array of…
We use a one-dimensional step model to study quantitatively the growth of step bunches on Si(111) surfaces induced by a direct heating current. Parameters in the model are fixed from experimental measurements near 900 deg C under the…
The vicinal Si(111) surface, inclined towards the [-1-12] direction, was investigated by scanning tunnelling microscopy and spot profile analysing low energy electron diffraction. It has been established that the surface, consisting of…
Taking advantage of vicinal (001) SrTiO3 substrates with different mean terrace widths, the heteroepitaxial growth of SrRuO3 in the step flow mode has been mapped as a function of mean step velocity. Transition between stable and unstable…