Line-tension model for plasticity as the Gamma-limit of a nonlinear dislocation energy

In this paper we rigorously derive a line-tension model for plasticity as the Gamma-limit of a nonlinear mesoscopic dislocation energy, without resorting to the introduction of an ad hoc cut-off radius. The Gamma-limit we obtain as the length of the Burgers vector tends to zero has the same form as the Gamma-limit obtained by starting from a linear, semi-discrete dislocation energy. The nonlinearity, however, creates several mathematical difficulties, which we tackled by proving suitable versions of the Rigidity Estimate in non-simply-connected domains and by performing a rigorous two-scale linearisation of the energy around an equilibrium configuration

A simple sufficient condition for the quasiconvexity of elastic stored-energy functions in spaces which allow for cavitation

In this note we formulate a sufficient condition for the quasiconvexity at $x \mapsto \lambda x$ of certain functionals $I(u)$ which model the stored-energy of elastic materials subject to a deformation $u$. The materials we consider may cavitate, and so we impose the well-known technical condition (INV), due to M\"{u}ller and Spector, on admissible deformations. Deformations obey the condition $u(x)= \lambda x$ whenever $x$ belongs to the boundary of the domain initially occupied by the material. In terms of the parameters of the models, our analysis provides an explicit upper bound on those $\lambda>0$ such that $I(u) \geq I(u_{\lambda})$ for all admissible $u$, where $u_{\lambda}$ is the linear map $x \mapsto \lambda x$ applied across the entire domain. This is the quasiconvexity condition referred to above

The Neumann sieve problem and dimensional reduction: a multiscale approach

We perform a multiscale analysis for the elastic energy of a $n$-dimensional bilayer thin film of thickness $2\delta$ whose layers are connected through an $\epsilon$-periodically distributed contact zone. Describing the contact zone as a union of $(n-1)$-dimensional balls of radius $r\ll \epsilon$ (the holes of the sieve) and assuming that $\delta \ll \epsilon$, we show that the asymptotic memory of the sieve (as $\epsilon \to 0$) is witnessed by the presence of an extra interfacial energy term. Moreover we find three different limit behaviors (or regimes) depending on the mutual vanishing rate of $\delta$ and $r$. We also give an explicit nonlinear capacitary-type formula for the interfacial energy density in each regime.Comment: 43 pages, 4 figure

Human adipose derived stem cells for corneal disorders

PURPOSE: The topical use of human ADSC was investigated for treating injured rat cornea. METHODS: Animals underwent corneal lesion and divided in 5 treatment groups: control, stem cells, serum, stem+serum, and adipose. Fluorescein positive defect area, light microscope and histological evaluation were considered. RESULTS: The stem cell treated eyes showed better epithelial healing confirmed by histology. CONCLUSIONS: Preliminary results show that ADSC treatment improves corneal wound healin

Geometric rigidity for incompatible fields and an application to strain-gradient plasticity

<p>In this paper we show that a strain-gradient plasticity model arises as the Gamma-limit of a nonlinear semi-discrete dislocation energy. We restrict our analysis to the case of plane elasticity, so that edge dislocations can be modelled as point singularities of the strain field.</p> <p>A key ingredient in the derivation is the extension of the rigidity estimate proved by Friesecke, James and Mueller to the case of fields with nonzero curl.</p&gt

Newer Intraocular Pressure Measurement Techniques

An elevated intraocular pressure (IOP) has been shown to be one of the major risk factors for glaucoma. It is of utmost importance to obtain accurate and precise IOP when dealing with patients with ocular hypertension and glaucoma, especially patients who have undergone ocular surgery. Goldmann applanation tonometer (GAT) was first introduced in the 1950s and is still currently considered as the gold standard to measure IOP. Although the reproducibility of GAT has shown to be quite good, its accuracy provides several limitations. In particular, IOP measurements taken with GAT have been demonstrated to be influenced by many corneal parameters, including central thickness, curvature, astigmatism and biomechanics. Other disadvantages of GAT include the need for local anesthetic drops, for fluorescein and for a slitlamp. Several different methods have been proposed to overcome the disadvantages found in GAT. The newer devices used as alternative tonometric methods include the iCare rebound tonometer, the BioResonator applanation resonance tonometer, the Pascal dynamic contour tonometer, the ocular response analyzer, the Corvis ST pachy-tonometer and Ocuton S. The precision and accuracy of these alternative tonometric methods in comparison with GAT have been reported and discussed