Asymptotic analysis of thin viscous plate model

Abstract

A cell membrane is a very complex medium, which is difficult to study. One of the simplest approaches is to assume it purely elastic or purely viscous. In this paper, we follow the second assumption and derive mathematical model of nearly-planar viscous plate evolving under action of applied forces. The obtained model is non-linear and covers both stretching and bending of the membrane. In contrast to analogous works on viscous sheets, we use a unique scale for velocity components and take a few first terms in asymptotic expansion. The developed approach can be used for description of the cell membrane with nanoparticles inserted.

SiO2 barrier layer influence on the glass composites with oxide nano films laser ablation destruction

“…The composites laser ablation destruction under the pulse laser radiation influence were studied at the experimental layout described in [10] and by the technique given in [4]. The YAG-Nd laser generated the radiation pulses at the 1064 nm wavelength of the 20 ns time duration and the pulse energy up to 0.15 J in the mode locking regime.…”

“…Nano films are applied to change of the optical characteristics -the increasing in the light transmission by the optical details or giving of the reflecting properties [1,4] to them. Such a film is obtained by the sol-gel technology including the contact of a filmforming solution with a glass substrate [3,[6][7][8][9][10]. The glass surface becomes covered by the oxide one-or multilayer nano films in this case.…”

On the metric graph model for flows in tubular nanostructures

“…Definition. Operator H is denoted as sign preserving on the graph Γ if the inequality u (x) u (x ) > 0 takes place for any nontrivial solution of equation (22). Here x, x are arbitrary points of Γ \ ∂Γ.…”

“…To get the corresponding linear one we can linearize it in the vicinity of some solution or simply neglect the nonlinear inertial terms. It is possible to obtain the 1D Navier-Stokes equation by the asymptotic procedure for 3D or 2D Navier-Stokes equations in thin tubes (see, e.g., [19][20][21][22]). It is also possible to study linear 2D or 3D Stokes equations in a system of narrow tubes and to consider the limiting procedure for tubes having widths tending to zero.…”