Related papers: Unstable vicinal crystal growth from cellular auto…
In this paper we focus on crystal surfaces led out of equilibrium by a growth or erosion process. As a consequence of that the surface may undergo morphological instabilities and develop a distinct structure: ondulations, mounds or…
The problem of metastability for a stochastic dynamics with a parallel updating rule is addressed in the Freidlin--Wentzel regime, namely, finite volume, small magnetic field, and small temperature. The model is characterized by the…
Cell size control and homeostasis is a major topic in cell biology yet to be fully understood. Several growth laws like the timer, adder, and sizer were proposed, and mathematical approaches that model cell growth and division were…
Bacterial growth and division generally occur by the process known as binary fission, in which the cells grow polarly until they divide into two daughter cells. Although this process is affected by factors that introduce stochastic…
An ab-initio numerical study of the density-dependent, evolutionary stable dispersal strategy is presented. The simulations are based on a simple discretei generation island model with four processes: reproduction, dispersal, competition…
Recent study suggests that the streaming instability, one of the leading mechanisms for driving the formation of planetesimals, may not be as efficient as previously thought. Under some disc conditions, the growth timescale of the…
Starting with a many-atom master equation of a kinetic, restricted solid-on-solid (KRSOS) model with external material deposition, we investigate nonlinear aspects of the passage to a mesoscale description for a crystal surface in 1+1…
Current molecular dynamic simulations of biomolecules using multiple time steps to update the slowingly changing force are hampered by an instability occuring at time step equal to half the period of the fastest vibrating mode. This has…
Inside living cells are complex mixtures of thousands of components. It is hopeless to try to characterise all the individual interactions in these mixtures. Thus, we develop a statistical approach to approximating them, and examine the…
The distinction between absolute and convective instabilities is well known in the context of hydrodynamics and plasma physics. In this Letter, we examine an epitaxial crystal growth model from this point of view and show that a…
We consider the curvature driven dynamics of a domain wall separating two equivalent states in systems displaying a modulational instability of a flat front. We derive an amplitude equation for the dynamics of the curvature close to the…
We consider a family of multi-phase Stefan problems for a certain 1-d model of cell-to-cell adhesion and diffusion, which takes the form of a nonlinear forward-backward parabolic equation. In each material phase the cell density stays…
It is known that an axisymmetric viscous film flowing down the outside of a thin vertical fiber becomes unstable to interfacial perturbations. We present an experimental study using fluids with different densities, surface tensions and…
The translation and shape deformations of a passive viscous Newtonian droplet immersed in an active nematic liquid crystal under circular confinement are analyzed using a linear stability analysis. We focus on the case of a sharply aligned…
We propose a one-dimensional model based on the Burton-Cabrera-Frank equations to describe the electromigration-induced step bunching instability on vicinal surfaces. The step drift resulting from atomic evaporation and/or deposition is…
Building on the striking similarity between the structure of the spindle during mitosis in living cells and nematic textures in confined liquid crystals, we use a continuum model of two-dimensional nematic liquid crystal droplets, to…
In the growth of bacterial colonies, a great variety of complex patterns are observed in experiments, depending on external conditions and the bacterial species. Typically, existing models employ systems of reaction-diffusion equations or…
The morphological development of step edge patterns in the presence of meandering instability during step flow growth is studied by simulations and numerical integration of a continuum model. It is demonstrated that the kink…
Faithful segregation of genetic material during cell division requires alignment of chromosomes between two spindle poles and attachment of their kinetochores to each of the poles. Failure of these complex dynamical processes leads to…
The Burton-Cabrera-Frank (BCF) model for the flow of line defects (steps) on crystal surfaces has offered useful insights into nanostructure evolution. This model has rested on phenomenological grounds. Our goal is to show via scaling…