Related papers: Scaling theory for two-dimensional single domain g…
We study the cosmological evolution of domain wall networks in two and three spatial dimensions in the radiation and matter eras using a large number of high-resolution field theory simulations with a large dynamical range. We investigate…
Computational sampling has been central to the sciences since the mid-20th century. While machine-learning-based approaches have recently enabled major advances, their behavior remains poorly understood, with limited theoretical control…
Graphene growth by chemical vapor deposition has received a lot of attention recently owing to the ease with which large area films can be grown, but growth of large domain or equivalently large grain size has not been reported yet. In this…
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…
This study employs molecular dynamics simulations to investigate droplet dynamics when a stationary droplet on a solid surface is struck by another droplet of similar size from above. The focus is on the jumping behavior of the merged…
We report on the growth of domains of standing waves in electroconvection in a nematic liquid crystal. An ac voltage is applied to the system, forming an initial state that consists of travelling striped patterns with two different…
We present results of numerical simulations to estimate scaling exponents associated with driven surface growth in two spatial dimensions. We have simulated the restricted solid--on--solid growth model and used the time and system size…
The stability of interfaces and the mechanisms of thin film growth on semiconductors are issues of central importance in electronic devices. These issues can only be understood through detailed study of the relevant microscopic processes.…
Growth of epitaxial graphene on the C-face of SiC has been investigated. Using a confinement controlled sublimation (CCS) method, we have achieved well controlled growth and been able to observe propagation of uniform monolayer graphene.…
Understanding and optimizing thin-film synthesis requires measuring the diffusion length $d_\alpha$ of adsorbed growth precursors. Despite technological advances, in-situ measurements of $d_\alpha$ are often unachievable due to harsh…
Shearing with a finite shear rate a compressed granular system results in a region of grains flowing over a compact, static assembly. Perforce this region is dilated to a degree that depends on the shear rate, the loading pressure, gravity,…
The surface morphologies of poly(chloro-p-xylylene) films were measured using atomic force microscopy and analyzed within the frame work of the dynamic scaling theory. The evolution of polymer films grown with fixed experimental parameters…
From the smallest biological systems to the largest cosmological structures, spatial domains undergo expansion and contraction. Within these growing domains, diffusive transport is a common phenomenon. Mathematical models have been widely…
We investigate the growth of a film of some element B on a substrate made of another substrance A in a model of molecular beam epitaxy. A vertical exchange mechanism allows the A-atoms to stay on the growing surface with a certain…
A continuum model for growth of solids is developed, considering adatom deposition, surface diffusion, and configuration dependent incorporation rate. For amorphous solids it is related to surface energy densities. The high adatom density…
Using high precision Monte Carlo simulations and a mean-field theory, we explore coarsening phenomena in a simple driven diffusive system. The model is reminiscent of vehicular traffic on a two-lane ring road. At sufficiently high density,…
A new slow growth formulation for DNS of wall-bounded turbulent flow is developed and demonstrated to enable extension of slow growth modeling concepts to complex boundary layer flows. As in previous slow growth approaches, the formulation…
We study several one dimensional step flow models. Numerical simulations show that the slope of the profile exhibits scaling in all cases. We apply a scaling ansatz to the various step flow models and investigate their long time evolution.…
We study the distribution of domain areas, areas enclosed by domain boundaries (''hulls''), and perimeters for curvature-driven two-dimensional coarsening, employing a combination of exact analysis and numerical studies, for various initial…
We study the interplay between surface roughening and phase separation during the growth of binary films. Already in 1+1 dimension, we find a variety of different scaling behaviors depending on how the two phenomena are coupled. In the most…