Related papers: On the definition of the domain growth rate consta…
Time correlations for KPZ growth in 1+1 dimensions are reconsidered. We discuss flat, curved, and stationary initial conditions and are interested in the covariance of the height as a function of time at a fixed point on the substrate. In…
We consider a macroscopic model for the growth of living tissues incorporating pressure-driven dispersal and pressure-modulated proliferation. Assuming a power-law relation between the mechanical pressure and the cell density, the model can…
We consider the drift and diffusion properties of periodically driven renewal processes. These processes are defined by a periodically time dependent waiting time distribution, which governs the interval between subsequent events. We show…
The static and dynamic roughenings of a growing crystalline facet is studied where the growth mechanism is controlled by a restricted-curvature (RC) geometry. A continuum equation, in analogy with the Kardar-Parisi-Zhang (KPZ) equation is…
We study dipolar bosons in a 1D optical lattice and identify a region in parameter space---strong coupling but relatively weak on-site repulsion---hosting a series of stable charge-density-wave (CDW) states whose low-energy excitations,…
The aim of this note is to present preliminary existence results for a system of cross-diffusion equations defined on a domain with moving boundaries, which model the evolution of the concentrations of different chemical species in a solid…
We consider minimal graphs u(x,y)>0 over unbounded domains D (with u vanishing on the boundary of D). Assuming D contains a sector properly containing a halfplane, we obtain estimates on growth and provide examples illustrating a range of…
The chemical step is an elementary pattern in chemically heterogeneous substrates, featuring two regions of different wettability separated by a sharp border. Within the framework of lubrication theory, we investigate droplet motion and the…
We investigate the long term behavior in terms of finite dimensional global and exponential attractors, as time goes to infinity, of solutions to a semilinear reaction-diffusion equation on non-smooth domains subject to nonlocal Robin…
Recent experiments have shown that the high temperature incommensurate (I) charge density wave (CDW) phase of 1T-TaS2 can be photoinduced from the lower temperature, nearly commensurate (NC) CDW state. Here we report a time-resolved x-ray…
Gas bubble growth as a result of diffusion flux of dissolved gas molecules from the surrounding supersaturated solution to the bubble surface is studied. The condition of the flux steadiness is revealed. A limitation from below on the…
We study the evolution of thick domain walls in the different models of cosmological inflation, in the matter-dominated and radiation-dominated universe, or more generally in the universe with the equation of state $p=w\rho$. We have found…
Chemical vapor deposition (CVD) is a widely used technique to grow solid materials with accurate control of layer thickness and composition. Under mass-transport-limited conditions, the surface of thin films thus produced grows in an…
A version of fractional diffusion on bounded domains, subject to 'homogeneous Dirichlet boundary conditions' is derived from a kinetic transport model with homogeneous inflow boundary conditions. For nonconvex domains, the result differs…
We simulated the growth of 2D islands with 2 kinds of diffusion atoms using the kinetic Monte- Carlo (kMC) method. As a result, we found that the slow atoms tend to create nuclei and determine the island volume distribution, along with…
We study the large deviations of current-type observables defined for Markov diffusion processes evolving in smooth bounded regions of $\mathbb{R}^d$ with reflections at the boundaries. We derive for these the correct boundary conditions…
This paper studies a longitudinal shape transformation model in which shapes are deformed in response to an internal growth potential that evolves according to an advection reaction diffusion process. This model extends prior works that…
We study the formation of domain walls in a phase transition in which an S_5\times Z_2 symmetry is spontaneously broken to S_3\times S_2. In one compact spatial dimension we observe the formation of a stable domain wall lattice. In two…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
We introduce a non-diffusive spatial coupling term into the replicator equation of evolutionary game theory. The spatial flux is based on motion due to local gradients in the relative fitness of each strategy, providing a game-dependent…