Related papers: Two-dimensional pattern formation in surfactant-me…
An important component in studying mathematical models in many biochemical systems, such as those found in developmental biology, is phase transition. The purpose of this work is to analyze the phase transition property of a…
We present a simple method for incorporating the surface tension effect into an iterative conformal mapping model of two-dimensional diffusion-limited aggregation. A curvature-dependent growth probability is introduced and the curvature is…
Adding grains at a single site on a flat substrate in the Abelian sandpile models produce beautiful complex patterns. We study in detail the pattern produced by adding grains on a two-dimensional square lattice with directed edges (each…
Shape transformations of epithelial tissues in three dimensions, which are crucial for embryonic development or in vitro organoid growth, can result from active forces generated within the cytoskeleton of the epithelial cells. How the…
Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its detailed curvature. Topology…
Growth-induced pattern formations in curved film-substrate structures have attracted extensive attentions recently. In most existing literature, the growth tensor is assumed to be homogeneous or piecewise homogeneous. In this paper, we aim…
We show that elongated nanowires can be grown on crystal surfaces by allowing large strained two-dimensional islands to desorb by varying the adatom supersaturation or chemical potential. The width of the wires formed in this process is…
The ability to predict the morphology of crystals formed by chemical reactions is of fundamental importance for the shape-controlled synthesis of nanostructures. Based on the atomistic mechanism for crystal growth under different driving…
Square lattice gas models for heteroepitaxial growth are studied by means of kinetic Monte Carlo simulations, in order to find a possible origin of anisotropic island shape observed in growth experiments of long organic molecules. When…
We study the patterns formed by adding $N$ sand-grains at a single site on an initial periodic background in the Abelian sandpile models, and relaxing the configuration. When the heights at all sites in the initial background are low…
We study the formation of the dynamic adsorption layer when a bubble is released in a tank containing water with a tiny amount of surfactant. The influence of the sorption kinetic constants is examined by comparing the experiments with…
We investigate the growth of two-dimensional (2D) crystals on fluctuating surfaces using a phase field crystal model that is relevant on atomic length and diffusive time scales. Motivated by recent experiments which achieved unprecedented…
In their Comment [arXiv:2102.03842], Haas et al. advance two hypotheses on the nature of the shape transformations observed in surfactant-stabilized emulsion droplets, as the theoretical models that us [Phys. Rev. Lett. 126, 038001 (2021)]…
During the directional solidification of peritectic alloys, two stable solid phases (parent and peritectic) grow competitively into a metastable liquid phase of larger impurity content than either solid phase. When the parent or both solid…
We consider two sequential models of deposition and aggregation for particles. The first model (No Diffusion) simulates surface diffusion through a deterministic capture area, while the second (Sequential Diffusion) allows the atoms to…
Studying shape changing thick surfaces induced by differential growth helps us understand morphogenesis in biology and offers opportunities for device design. While ideal 2D differential growth maps have been well studied for both isotropic…
In this paper, we have formulated a phase-field model based on the grand-potential functional for the simulation of precipitate growth in the presence of coherency stresses. In particular, we study the development of dendrite-like patterns…
We investigate the formation and the coarsening dynamics of islands in a strained epitaxial semi-conductor film. These islands are commonly observed in thin films undergoing a morphological instability due to the presence of the elasto…
Surface reconstructions can drastically modify growth kinetics during initial stages of epitaxial growth as well as during the process of surface equilibration after termination of growth. We investigate the effect of activation barriers…
Tissue growth can be modeled in two dimension by only using circular granular cells, which can grow and produce child. Linear spring-dashpot model is used to bind the cells with a cut-off interaction range of 1.1 times sum of radii of…