We derive a set of equations for the dynamics of evolving fluid membranes, such as cell membranes, in the presence of bulk fluids. We model the membrane as a surface endowed with a director field, which describes the local average orientation of the molecules on the membrane. A model for the elastic energy of a surface endowed with a director field is derived using liquid crystal theory. This e...

Red Blood Cell (RBC) suspended in aquatic buffer is trapped and deformed by the dual-beam optical tweezers in order to measure the elasticity of the cell’s membrane. In this experiment, the RBCs were in the natural form of biconcave disc shape. We modeled a highly focused trapping beam of numerical aperture NA=1.25 as a spherical wave with Gaussian intensity distribution in a stationary study m...

Connecting different theoretical approaches, curvature modulated sorting in lipid bilayers fixed on non-planar surfaces is investigated. First, we present a continuous model of lateral membrane dynamics, described by a nonlinear PDE of 4th order. We then prove the existence and uniqueness of solutions of the presented model and simulate membrane dynamics using a finite element approach. Adoptin...

Adsorption of proteins onto membranes can alter the local membrane curvature. This phenomenon has been observed in biological processes such as endocytosis, tubulation, and vesiculation. However, it is not clear how the local surface properties of the membrane, such as membrane tension, change in response to protein adsorption. In this article, we show that the partial differential equations ar...

Shear rate has been shown to critically affect the kinetics and receptor specificity of cell-cell interactions. In this study, the collision process between two modeled cells interacting in a linear shear flow is numerically investigated. The two identical biological or artificial cells are modeled as deformable capsules composed of an elastic membrane. The cell deformation and trajectories are...

To evaluate the earth seismic response due to earthquake effects, ground response analyses are used to predict ground surface motions for development of design response spectra, to compute dynamic stresses and strains for evaluation of liquefaction hazards, and to determine the earthquake induced forces that can lead to instability of earth and earth-retaining structures. Most of the analytical...

Herein paper compares the analytical model with the FEM based numerical model of the axisymmetric bending of circular sandwich plates. Also, the paper describes equations of the circular symmetrical sandwich plates bending with isotropic face sheets and the nonlinear elastic core material. The method of constructing an analytical solution of nonlinear differential equations has been described. ...

to evaluate the earth seismic response due to earthquake effects, ground response analyses are used to predict ground surface motions for development of design response spectra, to compute dynamic stresses and strains for evaluation of liquefaction hazards, and to determine the earthquake induced forces that can lead to instability of earth and earth-retaining structures. most of the analytical...

We explore the electric-field-induced interfacial instabilities of a trilayer composed of a thin elastic film confined between two viscous layers. A linear stability analysis (LSA) is performed to uncover the growth rate and length scale of the different unstable modes. Application of a normal external electric field on such a configuration can deform the two coupled elastic-viscous interfaces ...