Related papers: Pushing, blocking and polynuclear growth
We study height fluctuations of interfaces in the $(1+1)$-dimensional Kardar-Parisi-Zhang (KPZ) class, growing at different speeds in the left half and the right half of space. Carrying out simulations of the discrete polynuclear growth…
Habitat loss is one of the biggest threats facing plant species nowadays. We formulate a simple mathematical model of seed dispersal on reduced habitats to discuss survival of the species in relation to the habitat size and seeds production…
A finite temperature version of body-centered solid-on-solid growth models involving attachment and detachment of dimers is discussed in 1+1 dimensions. The dynamic exponent of the growing interface is studied numerically via the spectrum…
This paper concerns multiphase models of tumor growth in interaction with a surrounding tissue, taking into account also the interplay with diffusible nutrients feeding the cells. Models specialize in nonlinear systems of possibly…
We discuss the steady state dynamics of interfaces with periodic boundary conditions arising from body-centered solid-on-solid growth models in $1+1$ dimensions involving random aggregation of extended particles (dimers,…
The formation of interface from an initial sharp interface in polydisperse A/B blends is studied using the external potential dynamic method. The present model is a nonlocal coupling model as we take into account the correlation between…
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original…
We develop a theory of nucleation on top of two-dimensional islands bordered by steps with an additional energy barrier $\Delta E_S$ for descending atoms. The theory is based on the concept of the residence time of an adatom on the…
We study the joint asymptotic behavior of spacings between particles at the edge of multilevel Dyson Brownian motions, when the number of levels tends to infinity. Despite the global interactions between particles in multilevel Dyson…
We study a coarsening process of one-dimensional cell complexes. We show that if cell boundaries move with velocities proportional to the difference in size of neighboring cells, then the average cell size grows at a prescribed exponential…
We introduce and analyze a class of growing geometric random graphs that are invariant under rescaling of space and time. Directed connections between nodes are drawn according to influence zones that depend on node position in space and…
We compute the dynamical prefactor in the nucleation rate of bubbles or droplets in first order phase transitions for the case where both viscous damping and thermal dissipation are significant. This result, which generalizes previous work…
An unbounded one-dimensional solid-on-solid model with integer heights is studied. Unbounded here means that there is no a priori restrictions on the discret e gradient of the interface. The interaction Hamiltonian of the interface is given…
Using large-scale kinetic Monte-Carlo (KMC) simulations, we investigate the non-equilibrium surface growth of the fullerene C$_{60}$. Recently, we have presented a self-consistent set of energy barriers that describes the nucleation and…
Although recent research on social networks emphasizes microscopic dynamics such as retweets and social connectivity of an individual user, we focus on macroscopic growth dynamics of social network link formation. Rather than focusing on…
We study the macroscopic evolution of the growing cluster in the exactly solvable corner growth model with independent exponentially distributed waiting times. The rates of the exponentials are given by an addivitely separable function of…
One-dependent first passage percolation is a spreading process on a graph where the transmission time through each edge depends on the direct surroundings of the edge. In particular, the classical iid transmission time $L_{xy}$ is…
We study irreversible dimer nucleation on top of terraces during epitaxial growth in one and two dimensions, for all values of the step-edge barrier. The problem is solved exactly by transforming it into a first passage problem for a random…
We apply the recently introduced distribution of sign-times (DST) to non-equilibrium interface growth dynamics. We are able to treat within a unified picture the persistence properties of a large class of relaxational and noisy linear…
The emergence of clustering and coarsening in crowded ensembles of self-propelled agents is studied using a lattice model in one-dimension. The persistent exclusion process, where particles move at directions that change randomly at a low…