Related papers: On the Geometric Principles of Surface Growth
We have developed a continuum model that explains the complex surface shapes observed in epitaxial regrowth on micron scale gratings. This model describes the dependence of the surface morphology on film thickness and growth temperature in…
It is shown that, by imposing reparametrization invariance, one may derive a variety of stochastic equations describing the dynamics of surface growth and identify the physical processes responsible for the various terms. This approach…
Accretion of mineralized thin wall-like structures via localized growth along their edges is observed in a range of physical and biological systems ranging from molluscan and brachiopod shells to carbonate-silica composite precipitates. To…
A crystal surface which is miscut with respect to a high symmetry plane exhibits steps with a characteristic distance. It is argued that the continuum description of growth on such a surface, when desorption can be neglected, is given by…
A method based on the kinetics of adatoms on a growing surface under epitaxial growth at low temperature in (1+1) dimensions is proposed to obtain a closed form of local growth equation. It can be generalized to any growth problem as long…
Based on dynamical renormalization group (RG) calculations to the one-loop order, the surface growth described by a nonlinear stochastic conserved growth equation, {\partial h \over \partial t} = \pm \nu_2 \nabla^2 h + \lambda\nabla \cdot…
Surface growth, by association or dissociation of material on the boundaries of a body, is ubiquitous in both natural and engineering systems. It is the fundamental mechanism by which biological materials grow, starting from the level of a…
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…
A discrete solid-on-solid model of epitaxial growth is introduced which, in a simple manner, takes into account the effect of an Ehrlich-Schwoebel barrier at step edges as well as the local relaxation of incoming particles. Furthermore a…
Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of…
Growth occurs in a wide range of systems ranging from biological tissue to additive manufacturing. This work considers surface growth, in which mass is added to the boundary of a continuum body from the ambient medium or from within the…
We study unstable epitaxy on singular surfaces using continuum equations with a prescribed slope-dependent surface current. We derive scaling relations for the late stage of growth, where power law coarsening of the mound morphology is…
We propose a variational framework for accretive surface growth driven by an optimality principle. Rather than prescribing a kinetic law, the configuration at each time step is obtained, within a time-discrete setting, as the solution of a…
In this paper we present a generalization of a simple solid-on-solid epitaxial model of thin films growth, when surface morphology anisotropy is provoked by anisotropy in model control parameters: binding energy and/or diffusion barrier.…
In this work, a study of epitaxial growth was carried out by means of wavelets formalism. We showed the existence of a dynamic scaling form in wavelet discriminated linear MBE equation where diffusion and noise are the dominant effects. We…
A discussion of epitaxial growth is presented for those situations (OMVPE, CBE, ALE, MOMBE, GSMBE, etc.) when the kinetics of surface processes associated with molecular precursors may be rate limiting. Emphasis is placed on the…
Several aspects of the theory of epitaxial crystal growth from atomic or molecular beams are developed from the perspective of statistical physics. Lectures are devoted to the rate equation theory of two-dimensional nucleation and its…
The role of step edge diffusion (SED) in epitaxial growth is investigated. To this end we revisit and extend a recently introduced simple cubic solid-on-solid model, which exhibits the formation and coarsening of pyramid or mound like…
For the past two decades the Villain-Lai-Das Sarma equation has served as the theoretical framework for conserved surface growth processes, such as molecular-beam epitaxy. However some phenomena, such as mounding, are yet to be fully…
In this paper we formulate a geometric theory of the mechanics of growing solids. Bulk growth is modeled by a material manifold with an evolving metric. Time dependence of metric represents the evolution of the stress-free (natural)…