Related papers: Unstable vicinal crystal growth from cellular auto…
A one-dimensional cellular automaton with a probabilistic evolution rule can generate stochastic surface growth in $(1 + 1)$ dimensions. Two such discrete models of surface growth are constructed from a probabilistic cellular automaton…
For low to moderate supersaturations, crystals grow by lateral build-up of new layers. The edges of the layers are known as "steps". We consider the rate of step advance on a flat crystal face under the influence of bulk diffusion in the…
The step bunching instability is studied in three models of step motion defined in terms of ordinary differential equations (ODE). The source of instability in these models is step-step attraction, it is opposed by step-step repulsion and…
We revisit the diffusive instability in dusty disks that arises when the dust mass diffusivity and/or viscosity decreases sufficiently steeply with increasing dust density. Our updated model includes an incompressible, viscous gas that…
We introduce two hybrid models of step bunching on vicinal crystal surfaces. The model equations for step velocity are constructed by the two possible exchanges of terms between the equations of two primary models MM2 and LW2…
We report the results of computer simulations of epitaxial growth in the presence of a large Schwoebel barrier on different crystal surfaces: simple cubic(001), bcc(001), simple hexagonal(001) and hcp(001). We find, that mounds coarse by a…
Microbial growth and division are fundamental processes relevant to many areas of life science. Of particular interest are homeostasis mechanisms, which buffer growth and division from accumulating fluctuations over multiple cycles. These…
Epitaxial (001) BiFeO3 thin films grown on vicinal SrTiO3 substrates are under large anisotropic stress from the substrates. The variations of the crystallographic tilt angle and the c lattice constant, caused by the lattice mismatch, along…
Concerted experimental and numerical studies of step bunching on vicinal crystal surfaces resulting from step-down electromigration of partially charged adatoms, confirmed the theoretical prediction of scaling dependence of the minimal…
Two mechanisms for the breakdown of step flow growth, in the sense of the appearance of steps of opposite sign to the original vicinality, are studied by kinetic Monte Carlo simulations and scaling arguments. The first mechanism is the…
A system of coupled chaotic bistable maps on a lattice with randomly distributed impurities is investigated as a model for studying the phenomenon of phase growth in nonuniform media. The statistical properties of the system are…
We describe a novel crystal growth instability that enhances the development of thin edges, promoting the formation of plate-like or hollow columnar morphologies. This instability arises when diffusion-limited growth is coupled with…
The analysis of the Rayleigh-B\'enard instability due to the mass diffusion in a fluid-saturated horizontal porous layer is reconsidered. The standard diffusion theory based on the variance of the molecular position growing linearly in time…
We rigorously prove a form of disorder-resistance for a class of one-dimensional cellular automaton rules, including some that arise as boundary dynamics of two-dimensional solidification rules. Specifically, when started from a random…
During the early developmental process of organisms, the formation of the left-right laterality requires a subtle mechanism, as it is associated with other principal body axes. Any inherent chiral feature in an egg cell can in principal…
Cells achieve size homeostasis by regulating their division timing based on their size, added size, and cell cycle time. Previous research under steady-state conditions demonstrated the robustness of these mechanisms. However, their dynamic…
We study the steady state of an assembly of microtubules in a confined volume, analogous to the situation inside a cell where the cell boundary forms a natural barrier to growth. We show that the dynamical equations for growing and…
We study the continuum limit in 2+1 dimensions of nanoscale anisotropic diffusion processes on crystal surfaces relaxing to become flat below roughening. Our main result is a continuum law for the surface flux in terms of a new…
From the mitotic spindle up to tissues and biofilms, many biological systems behave as active droplets, which often break symmetry and change shape spontaneously. Here, I show that active nematic droplets can experience a fingering…
We present a simple mathematical model that captures the evolutionary capabilities of a prebiotic compartment or protocell. In the model the protocell contains an autocatalytic set whose chemical dynamics is coupled to the growth-division…