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

Stem Cell Therapy in Ocular Pathologies in the Past 20 Years

Stem cell therapies are successfully used in various fields of medicine. This new approach of research is also expanding in ophthalmology. Huge investments, resources and important clinical trials have been performed in stem cell research and in potential therapies. In recent years, great strides have been made in genetic research, which permitted and enhanced the differentiation of stem cells. Moreover, the possibility of exploiting stem cells from other districts (such as adipose, dental pulp, bone marrow stem cells, etc.) for the treatment of ophthalmic diseases, renders this topic fascinating. Furthermore, great strides have been made in biomedical engineering, which have proposed new materials and threedimensional structures useful for cell therapy of the eye. The encouraging results obtained on clinical trials conducted on animals have given a significant boost in the creation of study protocols also in humans. Results are limited to date, but clinical trials continue to evolve. Our attention is centered on the literature reported over the past 20 years, considering animal (the most represented in literature) and human clinical trials, which are limiting. The aim of our review is to present a brief overview of the main types of treatments based on stem cells in the field of ophthalmic pathologies

A Bridging Mechanism in the Homogenization of Brittle Composites with Soft Inclusions

We provide a homogenisation result for the energy-functional associated with a purely brittle composite whose microstructure is characterised by soft periodic inclusions embedded in a stiffer matrix. We show that the two constituents as above can be suitably arranged on a microscopic scale \u3b5 to obtain, in the limit as \u3b5 tends to zero, a homogeneous macroscopic energy-functional explicitly depending on the opening of the crack

How and when of eyelid reconstruction using autologous transplantation

Reconstructive surgery of the eyelid after tumor excision, trauma or other causes can be challenging, especially due to the complexities of the anatomic structures and to the necessity of both functional and aesthetic successful outcomes. The aim of this minireview was to investigate the use of tissue transplantation in eyelid reconstruction. Surgical procedures are various, based on the use of both flaps, pedicled or free, and grafts, in order to guarantee adequate tissue reconstruction and blood supply, which are necessary for correct healing. Common techniques normally include the use of local tissues, combining non-vascularized grafts with a vascularized flap for the two lamellae repair, to attempt a reconstruction similar to the original anatomy. When defects are too wide, vast, deep, and complex or when no adjacent healthy tissues are available, distant area tissues need to be recruited as free flaps or grafts and paired with mucosal layer reconstruction. With regards to the anterior lamella, full thickness skin grafts are commonly preferred. With regards to the reconstruction of posterior lamella, there are different graft options, which include conjunctival or tarsoconjunctival, mucosal or palatal or cartilaginous grafts usually combined with local flaps. Free flap transplantation, normally reserved for rare select cases, include the use of the radial forearm and anterolateral flaps combined with mucosal grafts, which are surgical options currently reported in the literature

Adipose Stem Cells in Modern-Day Ophthalmology

Stem cells (SCs) have evolved as an interesting and viable factor in ophthalmologic patient care in the past decades. SCs have been classified as either embryonic, mesenchymal, tissue-specific, or induced pluripotent cells. Multiple novel management techniques and clinical trials have been established to date. While available publications are predominantly animal-model-based, significant material is derived from human studies and case-selected scenarios. This possibility of explanting cells from viable tissue to regenerate/repair damaged tissue points to an exciting future of therapeutic options in all fields of medicine, and ophthalmology is surely not left out. Adipose tissue obtained from lipo-aspirates has been shown to produce mesenchymal SCs that are potentially useful in different body parts, including the oculo-visual system. An overview of the anatomy, physiology, and extraction process for adipose-tissue-derived stem cells (ADSC) is important for better understanding the potential therapeutic benefits. This review examines published data on ADSCs in immune-modulatory, therapeutic, and regenerative treatments. We also look at the future of ADSC applications for ophthalmic patient care. The adverse effects of this relatively novel therapy are also discussed

A global method for deterministic and stochastic homogenisation in BV

In this paper we study the deterministic and stochastic homogenisation of free-discontinuity functionals under linear growth and coercivity conditions. The main novelty of our deterministic result is that we work under very general assumptions on the integrands which, in particular, are not required to be periodic in the space variable. Combining this result with the pointwise Subadditive Ergodic Theorem by Akcoglu and Krengel, we prove a stochastic homogenisation result, in the case of stationary random integrands. In particular, we characterise the limit integrands in terms of asymptotic cell formulas, as in the classical case of periodic homogenisation

Thermo-electrochemical production of compressed hydrogen from methane with near-zero energy loss

[EN] Conventional production of hydrogen requires large industrial plants to minimize energy losses and capital costs associated with steam reforming, water-gas shift, product separation and compression. Here we present a protonic membrane reformer (PMR) that produces high-purity hydrogen from steam methane reforming in a single-stage process with near-zero energy loss. We use a BaZrO3-based proton-conducting electrolyte deposited as a dense film on a porous Ni composite electrode with dual function as a reforming catalyst. At 800 degrees C, we achieve full methane conversion by removing 99% of the formed hydrogen, which is simultaneously compressed electrochemically up to 50 bar. A thermally balanced operation regime is achieved by coupling several thermo-chemical processes. Modelling of a small-scale (10 kg H-2 day-1) hydrogen plant reveals an overall energy efficiency of >87%. 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The Neumann sieve problem and dimensional reduction: a multi-scale approach

43 pages, 4 figuresInternational audienceWe 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