On the metric graph model for flows in tubular nanostructures

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.

Geometrical analyses of nanostructures

“…Substituting (10) and 13into 8, we finally obtain the connection between configurationally volumes of triclinic and rectangular cell:…”

“…The geometrical form of produced nanostructures is rectangular (thin films, quantum rods and quantum parallelepiped) or cylindrical (cylinders with nanocross-section and macroscopic height and cylinders having nanoheight and nanocross-section). Mentioned geometrical forms enable correct inclusion of boundary conditions into evaluations [3][4][5][6][7][8][9][10].…”

Mathematical Model for Axisymmetric Taylor Flows Inside a Drop

“…Solutions of the Stokes equations for two-dimensional flows inside an elliptic region were considered in article [22]. A similar approach is used for three-dimensional flows in cases where the boundary has a spherical or cylindrical shape [27,28].…”

Green's function method for time-fractional diffusion equation on the star graph with equal bonds

“…In [16] authors proposed the model of time-dependent geometric graph for description of the dynamical Casimir effect. In [17], the authors used metric graph approximation for investigation of strong variation of the viscosity and density in cylindrical domains of the small radius. And paper [18] devoted to an explicitly solvable model for periodic chain of coupled disks.…”