Cells in an epithelial monolayer coordinate motion with their neighbors giving rise to collectively moving packs of sizes spanning multiple cell diameters. The physical mechanism controlling the pack size, however, remains unclear. A potential comes from assuming that cell–substrate traction forces persist over some time scale: large enough persistence time, collective emerge. To test this hypo...

inthis paper, the main aim is to introduce the class $mathcal{u}_p(lambda,alpha,beta,k_0)$ of $p$-harmonic mappings togetherwith its subclasses $mathcal{u}_p(lambda,alpha,beta,k_0)capmathcal {t}_p$ and $mathcal{u}_p(lambda,alpha,beta,k_0)capmathcal {t}_p^0$, andinvestigate the properties of the mappings in these classes. first,we give a sufficient condition for mappings to be in $mathcal{u}_p(l...

Closed form expressions are developed for the thermoelastic curvature of the initially plane end faces of a traction free cylinder subjected to arbitrary axisymmetric heat flux, the curved surfaces being assumed insulated. The solution is developed from a potential function representation of displacement and temperature for an elastic layer. The reciprocal theorem is invoked to show that the tr...

The effect of damage due to particle debonding on the constitutive response of highly filled composites is investigated using two multiscale homogenization schemes: one based on a closed-form micromechanics solution, and the other on the finite element implementation of the mathematical theory of homogenization. In both cases, the particle debonding process is modeled using a bilinear cohesive ...

This paper considers the effect of surface charges on the surface instability of thin conductive liquid films. A characteristic relation is obtained for determining the wave number of the fastest growing mode as a function of surface tension, dispersive van der Waals force, and electrostatic tractions exerted by the film surface charges. Two natural length scales of the microsystem are further ...

We propose two models for pattern formation in early embryogenesis. The first deals with patterns in motile mesenchymal cells; the second treats patterns in epithelial sheets. In the mesenchymal model, cells exert tractions which deform the extracellular matrix within which they move. This in turn affects their motion. The model field equations are formulated and analysed, and applied to two wi...

Abstract. We study a moving boundary value problem consisting of a viscous incompressible fluid moving and interacting with a nonlinear elastic fluid shell. The fluid motion is governed by the Navier-Stokes equations, while the fluid shell is modeled by a bending energy which extremizes the Willmore functional and a membrane energy that extremizes the surface area of the shell. The fluid flow a...