We consider a free boundary problem modeling electrostatic microelectromechanical systems. The model consists of a fourth-order damped wave equation for the elastic plate displacement which is coupled to an elliptic equation for the electrostatic potential. We first review some recent results on existence and nonexistence of steady-states as well as on local and global well-posedness of the dyn...

The impact of a two-dimensional elastic disk with a wall is numerically studied. It is clarified that the coefficient of restitution (COR) decreases with the impact velocity. The result is not consistent with the recent quasi-static theory of inelastic collisions even for very slow impact. This suggests that the elastic model cannot be used in the quasi-static limit. A new quasi-static theory o...

In this paper we prove the existence of all moments of the solutions to the time-dependent spatially homogeneous transport equation describing elastic and inelastic scattering of particles. The proof uses the theory of resolvent positive operators and Desch’s perturbation theorem. As an application we carry out the asymptotic analysis of the full transport equation with dominant elastic scatter...

This paper discusses the influence of fiber orientation on elastic limit tensile stress ultra-high performance reinforced cementitious composites (UHPFRC). An original model relating to is proposed, and three determination methods are compared. Five specimens tested under uniaxial tension characterized with digital image correlation, acoustic emission displacement transducers. Before testing, d...

By combining molecular dynamics simulations and analytical arguments, we investigate the elastic properties of charged lipid bilayers. We show that electrostatic interactions between the head groups can lead to solidification of the lipid bilayer that would otherwise be in a liquid state if the charges were absent. All elastic parameters of the bilayer such as the bending rigidity κ and the two...

Two coupled nonlinear Klein-Gordon equations modeling the three-dimensional dynamics of a twisted elastic rod near its first bifurcation threshold are analyzed. First, it is shown that these equations are Hamiltonian and that they admit a 2-parameter family of traveling wave solutions. Second, special solutions corresponding to simple deformations of the elastic rod are considered. The stabilit...

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...

Recent experiments have demonstrated that the nonlinear elasticity of in vitro networks of the biopolymer actin is dramatically altered in the presence of a flexible cross-linker such as the cytoskeletal protein filamin. The basic principles governing the mechanical properties of such networks, however, remain poorly understood. Here we describe an effective medium theory of flexibly cross-link...

To explore the role of titin filaments in muscle elasticity, we measured the resting tension-sarcomere length curves of six rabbit skeletal muscles that express three size classes of titin isoform. The stress-strain curves of the split fibers of these muscles displayed a similar multiphasic shape, with an exponential increase in tension at low sarcomere strain followed by a leveling of tension ...

We study the organization of topological defects in a system of nematogens confined to the two-dimensional sphere (S2). We first perform Monte Carlo simulations of a fluid system of hard rods (spherocylinders) living in the tangent plane of S2. The sphere is adiabatically compressed until we reach a jammed nematic state with maximum packing density. The nematic state exhibits four +1/2 disclina...