Models of the formation of nanorolls in fluid media are constructed. The successive stages of the detachment of a stressed double nanolayer with the subsequent twisting into a nanoroll are calculated by the molecular dynamics method. The dynamics of twisting with the formation of a multiwalled nanoroll is described within a continuous model. The results of simulating the formation of different configurations of nanorolls during their diffusion growth are reported.

Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphsThe quantum graph having the form of branching strips with hexagonal (honeycomb) structure is considered. The Hamiltonian is determined as free 1D Schrödinger operator on each edge and some "boundary" conditions at each vertex. We obtain the conditions ensuring the point spectrum's existence for the Schrödinger operator of the system and relations that give us the eigenvalues. C 2014 AIP Publishing LLC.

No abstract

A metric graph model is suggested for the Stokes flow concentrated in the vicinity of a network embedded in R 3. As a basic problem, we consider the case corresponding to strong variation of the viscosity and density in a cylinder of small radius. An equation for the main term of the asymptotics is obtained. As for a graph structure, coupling conditions are assumed at the graph vertices.

No abstract