A new space semi-discretization for the dynamic Signorini problem, based on a modification of the mass term, has been recently proposed. We prove the convergence of the space semi-discrete solutions to a solution of the continuous problem in the case of a visco-elastic material.

We investigate some critical models for visco-elastic flows of Oldroyd-B type in dimension two. We use a transformation which exploits the Oldroyd-B structure to prove an L∞ bound on the vorticity which allows us to prove global regularity for our systems.

We propose a new reduced model for gravity-driven free-surface flows of shallow elastic fluids. It is obtained by an asymptotic expansion of the upper-convected Maxwell model for elastic fluids. The viscosity is assumed small (of order epsilon, the aspect ratio of the thin layer of fluid), but the relaxation time is kept finite. Additionally to the classical layer depth and velocity in shallow ...

A problem of reflection and transmission of a plane shear wave incident at a corrugated interface between transversely isotropic inhomogeneous and visco-elastic half-spaces is investigated. Applying appropriate boundary conditions and using Rayleigh’s method of approximation expressions for reflection and transmission coefficients are obtained for the first and second order approximation of the...

A new space semi-discretization for the dynamic Signorini problem, based on a modification of the mass term, has been recently proposed. We prove the convergence of the space semi-discrete solutions to a solution of the continuous problem in the case of a visco-elastic material.

Robotic grasps exhibiting visco-elastic contact interactions with the manipulated object are considered. Control of internal forces is investigated. The presence of nonnegligible compliance at contacts, implies that the object dynamics cannot be neglected when attempting to control internal forces without affecting the object position. A dynamic internal force control is proposed. It is decoupl...

Using a general theory for evolution inclusions, existence and uniqueness theorems are obtained for weak solutions to a frictional dynamic contact problem for elastic visco-plastic material. An existence theorem in the case where the friction coefficient is discontinuous is also presented.

Abstract We develop a geometric formulation of fluid dynamics, valid on arbitrary Riemannian manifolds, that regards the momentum-flux and stress tensors as 1-form-valued 2-forms, their divergence covariant exterior derivative. review necessary tools differential geometry obtain corresponding coordinate-free form equations motion for variety inviscid models—compressible incompressible Euler equ...

A Cylindrical two layer fluid model for the transport of serous and mucus layer in the human trachea and the steady state condition due to cilia beating, some immotile cilia forming porous bed in serous sub -layer in contact with the epithelium and air motion by considering mucus as a visco-elastic fluid are studied. The effect of air-motion due to forced expiration and other processes is consi...