Kinetic models of quantum size effect-directed nanocluster self-assembly in atomic corrals.

Two simple kinetic models of quantum size effect-directed nanocluster self-assembly in circular atomic corrals are discussed. The models correspond to an adsorption (either a physisorption or a chemisorption) and an adsorption-diffusion regimes that are typical at low and high temperatures, respectively. Small magnitudes of a variation of the electronic local density of states is shown to be the prime factor that impedes self-assembly in the latter regime.

Model for computing kinetics of the graphene edge epitaxial growth on copper.

A basic kinetic model that incorporates a coupled dynamics of the carbon atoms and dimers on a copper surface is used to compute growth of a single-layer graphene island. The speed of the island's edge advancement on Cu[111] and Cu[100] surfaces is computed as a function of the growth temperature and pressure. Spatially resolved concentration profiles of the atoms and dimers are determined, and the contributions provided by these species to the growth speed are discussed.

Marangoni convection in a thin film on a vertically oscillating plate.

Thermocapillary (Marangoni) convection in a thin film on a plate oscillating with a frequency ranging from ultralow to high is considered. By adjusting the vibration amplitude, the impact of the vibration is kept non-negligible. Using the long-wave approximation framework, the amplitude equations are derived for each frequency interval, and linear and weakly nonlinear stability analyses are performed, supplemented by computations where necessary.

Long-wave model for strongly anisotropic growth of a crystal step.

A continuum model for the dynamics of a single step with the strongly anisotropic line energy is formulated and analyzed. The step grows by attachment of adatoms from the lower terrace, onto which atoms adsorb from a vapor phase or from a molecular beam, and the desorption is nonnegligible (the "one-sided" model). Via a multiscale expansion, we derived a long-wave, strongly nonlinear, and strongly anisotropic evolution PDE for the step profile.

Long-wave Marangoni convection in a thin film heated from below.

We consider long-wave Marangoni convection in a liquid layer atop a substrate of low thermal conductivity, heated from below. We demonstrate that the critical perturbations are materialized at the wave number K ∼ √Bi, where Bi is the Biot number which characterizes the weak heat flux from the free surface. In addition to the conventional monotonic mode, a novel oscillatory mode is found.