Related papers: A Discrete Model for Nonequilibrium Growth Under S…
Inelastic surface growth associated with continuous creation of incompatibility on the boundary of an evolving body is behind a variety of natural and technological processes, including embryonic development and 3D printing. In this paper…
A systematic understanding of the evolution and growth dynamics of invasive solid tumors in response to different chemotherapy strategies is crucial for the development of individually optimized oncotherapy. Here, we develop a hybrid…
We investigate the influence of step edge diffusion (SED) and desorption on Molecular Beam Epitaxy (MBE) using kinetic Monte-Carlo simulations of the solid-on-solid (SOS) model. Based on these investigations we propose two strategies to…
In this work, we apply phase field simulations to examine the coarsening behavior of morphologically complex two-phase microstructures in which the phases have highly dissimilar mobilities, a condition approaching that found in experimental…
Crystal surfaces may undergo thermodynamical as well kinetic, out-of-equilibrium instabilities. We consider the case of mound and pyramid formation, a common phenomenon in crystal growth and a long-standing problem in the field of pattern…
Aqueous foams coarsen with time due to gas diffusion through the liquid. The mean bubble size grows, and small bubbles vanish. However, coarsening is little understood for foams with an intermediate liquid content, particularly in the…
Instabilities of fluid-fluid interfaces are ubiquitous in passive soft matter. Adding activity to the interface or either fluid can dramatically change the stability of the interface. Using experiment and theory, we investigate the…
Dynamic wetting poses a well-known challenge in classical sharp-interface formulation as the no-slip wall condition leads to a contact line singularity that is typically regularized with a Navier boundary condition, often requiring…
Two phase solid-fluid mixture models are ubiquitous in biological applications. For instance, models for growth of tissues and biofilms combine time dependent and quasi-stationary boundary value problems set in domains whose boundary moves…
A class of nonequilibrium models with short-range interactions and sequential updates is presented. The models describe one dimensional growth processes which display a roughening transition between a smooth and a rough phase. This…
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…
We derive a stochastic nonlinear continuum theory to describe the morphological evolution of amorphous surfaces eroded by ion bombardment. Starting from Sigmund's theory of sputter erosion, we calculate the coefficients appearing in the…
We introduce and investigate the stochastic dynamics of the density of local extrema (minima and maxima) of non-equilibrium surface fluctuations. We give a number of exact, analytic results for interface fluctuations described by linear…
We consider a continuum mathematical model of biological tissue formation inspired by recent experiments describing thin tissue growth in 3D-printed bioscaffolds. The continuum model involves a partial differential equation describing the…
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…
We examine the applicability of the continuum model to describe the surface morphology of a hetero-growth system: compositionally-graded, relaxed GeSi films on (001) Si substrates. Surface roughness versus lateral dimension was analyzed for…
The restricted solid-on-solid (RSOS) model is a model of continuous-time surface growth characterized by the constraint that adjacent height differences are bounded by a fixed constant. Though the model is conjectured to belong to the KPZ…
The evolution of two grains, which lie on a substrate and are in contact with each other, can be roughly described by a model in which the exterior surfaces of the grains evolve by surface diffusion and the grain boundary, namely the…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
An interface description and numerical simulations of model A kinetics are used for the first time to investigate the intra-surface kinetics of phase ordering on corrugated surfaces. Geometrical dynamical equations are derived for the…