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The reported spatial variation in the fine-structure constant at high redshift, if physical, could be due to the presence of dilatonic domains, and one or more domain walls inside our horizon. An absorption spectrum of an object in a…
We study domain coarsening of two dimensional stripe patterns by numerically solving the Swift-Hohenberg model of Rayleigh-Benard convection. Near the bifurcation threshold, the evolution of disordered configurations is dominated by grain…
In this work an activator-depleted reaction-diffusion system is investigated on polar coordinates with the aim of exploring the relationship and the corresponding influence of domain size on the types of possible diffusion-driven…
Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is…
The geometry of fracture patterns in a dilute elastic network is explored using molecular dynamics simulation. The network in two dimensions is subjected to a uniform strain which drives the fracture to develop by the growth and coalescence…
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…
The morphological scaling properties of linear polymer films grown by vapor deposition polymerization (VDP) are studied by 1+1D Monte Carlo simulations. The model implements the basic processes of random angle ballistic deposition ($F$),…
Among living organisms, there are species that change their patterns on their body surface during their growth process and those that maintain their patterns. Theoretically, it has been shown that large-scale species do not form distinct…
Pattern formation has been extensively studied in the context of evolving (time-dependent) domains in recent years, with domain growth implicated in ameliorating problems of pattern robustness and selection, in addition to more realistic…
We study steady-state thin films on a chemically heterogeneous substrates of finite size, subject to no-flux boundary conditions. Based on the structure of the bifurcation diagram, we classify the one-dimensional steady-state solutions that…
Short time existence for a surface diffusion evolution equation with curvature regularization is proved in the context of epitaxially strained three-dimensional films. This is achieved by implementing a minimizing movement scheme, which is…
In crystal growth, surfactants are additive molecules used in dilute amount or as dense, permeable layers to control surface morphologies. Here, we investigate the properties of a strikingly different surfactant: a two-dimensional and…
We investigate the single-file dynamics of a tagged particle in a system consisting of N hardcore interacting particles (the particles cannot pass each other) which are diffusing in a one-dimensional system where the particles have…
Inhomogeneities in deposition may lead to formation of rough surfaces, whose height fluctuations can be probed directly by scanning microscopy, or indirectly by scattering. Analytical or numerical treatments of simple growth models suggest…
The growth of a crystal is usually determined by its surface. Many factors influence the growth dynamics. Energy barriers associated with the presence of steps most often decide about the emerging pattern. The height and type of…
Understanding the influence that copper substrate surface symmetry and oxygen impurities have on the growth of graphene by chemical vapor deposition is important for developing techniques for producing high quality graphene. Therefore, we…
A dissipative particle dynamics (DPD) model for the quantitative simulation of biofilm growth controlled by substrate (nutrient) consumption, advective and diffusive substrate transport, and hydrodynamic interactions with fluid flow…
We study statistical scale invariance and dynamic scaling in a simple solid-on-solid 2+1 - dimensional limited mobility discrete model of nonequilibrium surface growth, which we believe should describe the low temperature kinetic roughening…
Reaction--diffusion mechanism are a robust paradigm that can be used to represent many biological and physical phenomena over multiple spatial scales. Applications include intracellular dynamics, the migration of cells and the patterns…
We investigate the growth of the graphene buffer layer and the involved step bunching behavior of the silicon carbide substrate surface using atomic force microscopy. The formation of local buffer layer domains are identified to be the…