‎‎‎in this paper‎, ‎we develop multi-step methods to solve a class of two-dimensional nonlinear volterra integral equations (2d-nvies) of the first kind‎. ‎here‎, ‎we convert a 2d-nvie of the first kind to a one-dimensional linear vie of the first kind and then we solve the resulted equation numerically by multi-step methods‎. ‎we also verify convergence and error analysis of the method‎. ‎at t...

The aim of this paper is to extend, to the linear elasticity system, the asymptotic analysis by compensated compactness previously developed by the authors for the linear diffusion equation. For simplicity, we restrict ourselves to stratified media. In the case of sole homogenization we recover the classical result of W.H. Mc Connel, deriving explicitly the effective elasticity tensor for strat...

Three-dimensional (3D) cell cultures represent fundamental tools for the comprehension of cellular phenomena both in normal and in pathological conditions. In particular, mechanical and chemical stimuli play a relevant role on cell fate, cancer onset and malignant evolution. Here, we use mechanically-tuned alginate hydrogels to study the role of substrate elasticity on breast adenocarcinoma cel...

‎In this paper we study the dynamics of the 2D-motion of a particle of monolayer‎. First we consider the usual physical time component and the plan manifold R2, having the polar coordinates. Then a geometric approach to nonholonomic constrained mechanical systems is applied to a problem from the two dimensional geometric dynamics of the Langmuir-Blodgett monolayer‎. We consider a constraint sub...

In this paper, we construct, in a unified fashion, lower order finite element subspaces of spaces of symmetric tensors with square-integrable divergence on a domain in any dimension. These subspaces are essentially the symmetric H(div) − Pk (1 ≤ k ≤ n) tensor spaces, enriched, for each n − 1 dimensional simplex, by (n+1)n 2 H(div) − Pn+1 bubble functions when 1 ≤ k ≤ n − 1, and by (n−1)n 2 H(di...