Related papers: Conserved Growth on Vicinal Surfaces
We study a recently proposed nonlinear evolution equation describing the collective step meander on a vicinal surface subject to the Bales-Zangwill growth instability [O. Pierre-Louis et al., Phys. Rev. Lett. (80), 4221 (1998)]. A careful…
We investigate the nonlinear evolution of the Bales-Zangwill instability, responsible for the meandering of atomic steps on a growing vicinal surface. We develop an asymptotic method to derive, in the continuous limit, an evolution equation…
We propose a novel approach to continuum modeling of the dynamics of crystal surfaces. Our model follows the evolution of an ensemble of step configurations, which are consistent with the macroscopic surface profile. Contrary to the usual…
A limited mobility nonequilibrium solid-on-solid dynamical model for kinetic surface growth is introduced as a simple description for the morphological evolution of a growing interface under random vapor deposition and surface diffusion…
The steps at the crystal surfaces could be transparent for the migrating adatoms. In the case of significant transparency the velocity of a given step in a given moment is affected by detachment of atoms from rather distant steps in rather…
We present a theory for the damping of layer-by-layer growth oscillations in molecular beam epitaxy. The surface becomes rough on distances larger than a layer coherence length which is substantially larger than the diffusion length. The…
We propose a novel approach to continuum modelling of dynamics of crystal surfaces. Our model follows the evolution of an ensemble of step configurations, which are consistent with the macroscopic surface profile. Contrary to the usual…
We present a constitutive model capturing some of the experimentally observed features of soft biological tissues: nonlinear viscoelasticity, nonlinear elastic anisotropy, and nonlinear viscous anisotropy. For this model we derive the…
A high-symmetry crystal surface may undergo a kinetic instability during the growth, such that its late stage evolution resembles a phase separation process. This parallel is rigorous in one dimension, if the conserved surface current is…
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…
We extend our 2+1 dimensional discrete growth model (PRE 79, 021125 (2009)) with conserved, local exchange dynamics of octahedra, describing surface diffusion. A roughening process was realized by uphill diffusion and curvature dependence.…
The morphology of a growing crystal surface is studied in the case of an unstable two-dimensional step flow. Competition between bunching and meandering of steps leads to a variety of patterns characterized by their respective instability…
We generalize the surface growth model of Gates and Westcott to arbitrary inclination. The exact steady growth velocity is of saddle type with principal curvatures of opposite sign. According to Wolf this implies logarithmic height…
The static and dynamic roughenings of a growing crystalline facet is studied where the growth mechanism is controlled by a restricted-curvature (RC) geometry. A continuum equation, in analogy with the Kardar-Parisi-Zhang (KPZ) equation is…
Scanning tunneling microscopy experiments show that the unstable growth morphology observed during molecular beam homoepitaxy on slightly vicinal Si(001) surfaces consists of straight step bunches. The instability occurs under step- flow…
In this paper I study a model for a growing surface in the presence of anomalous diffusion, also known as the Fractal Kardar-Parisi-Zhang equation (FKPZ). This equation includes a fractional Laplacian that accounts for the possibility that…
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…
Mounding instability in a conserved growth from vapor is analysed within the framework of adatom kinetics on the growing surface. The analysis shows that depending on the local structure on the surface, kinetics of adatoms may vary, leading…
Substrate disorder effects on the scaling properties of growing crystalline surfaces in solidification or epitaxial deposition processes are investigated. Within the harmonic approach there is a phase transition into a low-temperature…
A continuum growth equation in 1+1 dimensions is obtained by considering the contributions to the underlying current from kinetics of adatoms on the surface. These considerations reproduce the slope dependent term that represents a stable…