Geometric and variational aspects of thin structures in nonsimple continua

This thesis concerns problems of looking for minimal energy shape in thin structures and of characterizing their deformations, pattern formation and possible instabilities, in particular for membranes and rods. More precisely, we develop here the study of some variational problems and geometric formulations for the mutual or self-interplay of these systems. The thesis aims to bring together notions from several mathematical fields in order to physically clarify the phenomena under attention and mathematically state their description. Thin structures are widespread in nature and biological architectures, from microscopic level like proteins and cells, to a macroscopic one, for example the brain, the epithelium or organs. In addition to these, also recent technological developments exploit their flexibility, just thinking of screens, lenses, composite materials or any kind of elastic filament. As regards membranes, we prove the existence of equilibrium configurations for a surface made of nematic crystals with precise boundary conditions and we capture some new and interesting properties of the solutions. On the other hand, concerning rods, we discuss the state of art about the notions of self-contact and non-interpenetration of matter and we develop a new energy functional in order to provide a novel approach to this physical constraint. The main results for this construction generalize the statements of works obtained in the last three decades for knots to tubular neighbourhoods of regular curves. We then proceed to show the existence and uniqueness of critical points for a system composed by an elastic Kirchhoff rod spanned by a liquid film taking into consideration, with respect to the classical formulation of the problem, an additional term that depends on the thickness of the cross-section of the rod. Finally, we study the surface instabilities of a soft bilayer composed of two different materials, where in particular the exterior one is a compressible membrane. We set the problem in a cylindrical geometry and we apply to the whole structure a uniaxial tension. Thanks to classical strategies of incremental elasticity we show that the expected formation of wrinkling patterns takes place in a precise direction and develops with different properties depending on the influence of the material parameters of the interacting materials.This thesis concerns problems of looking for minimal energy shape in thin structures and of characterizing their deformations, pattern formation and possible instabilities, in particular for membranes and rods. More precisely, we develop here the study of some variational problems and geometric formulations for the mutual or self-interplay of these systems. The thesis aims to bring together notions from several mathematical fields in order to physically clarify the phenomena under attention and mathematically state their description. Thin structures are widespread in nature and biological architectures, from microscopic level like proteins and cells, to a macroscopic one, for example the brain, the epithelium or organs. In addition to these, also recent technological developments exploit their flexibility, just thinking of screens, lenses, composite materials or any kind of elastic filament. As regards membranes, we prove the existence of equilibrium configurations for a surface made of nematic crystals with precise boundary conditions and we capture some new and interesting properties of the solutions. On the other hand, concerning rods, we discuss the state of art about the notions of self-contact and non-interpenetration of matter and we develop a new energy functional in order to provide a novel approach to this physical constraint. The main results for this construction generalize the statements of works obtained in the last three decades for knots to tubular neighbourhoods of regular curves. We then proceed to show the existence and uniqueness of critical points for a system composed by an elastic Kirchhoff rod spanned by a liquid film taking into consideration, with respect to the classical formulation of the problem, an additional term that depends on the thickness of the cross-section of the rod. Finally, we study the surface instabilities of a soft bilayer composed of two different materials, where in particular the exterior one is a compressible membrane. We set the problem in a cylindrical geometry and we apply to the whole structure a uniaxial tension. Thanks to classical strategies of incremental elasticity we show that the expected formation of wrinkling patterns takes place in a precise direction and develops with different properties depending on the influence of the material parameters of the interacting materials

Effects of surface tension and elasticity on critical points of the Kirchhoff-Plateau problem

We introduce a modified Kirchhoff-Plateau problem adding an energy term to penalize shape modifications of the cross-sections appended to the elastic midline. In a specific setting, we characterize quantitatively some properties of minimizers. Indeed, choosing three different geometrical shapes for the cross-section, we derive Euler-Lagrange equations for a planar version of the Kirchhoff-Plateau problem. We show that in the physical range of the parameters, there exists a unique critical point satisfying the imposed constraints. Finally, we analyze the effects of the surface tension on the shape of the cross-sections at the equilibrium

A variational analysis of nematic axisymmetric films: the covariant derivative case

Nematic surfaces are thin fluid structures, ideally two-dimensional, endowed with an in-plane nematic order. In 2012, two variational models have been introduced by Giomi [10] and by Napoli and Vergori [27,26]. Both penalize the area of the surface and the gradient of the director: in [10] the covariant derivative of the director is considered, while [26] deals with the surface gradient. In this paper, a complete variational analysis of the model proposed by Giomi is performed for revolution surfaces spanning two coaxial rings

Thermal convection in a higher velocity gradient and higher temperature gradient fluid

We analyse a model for thermal convection in a class of generalized Navier-Stokes equations containing fourth order spatial derivatives of the velocity and of the temperature. The work generalises the isothermal model of A. Musesti. We derive critical Rayleigh and wavenumbers for the onset of convective fluid motion paying careful attention to the variation of coefficients of the highest derivatives. In addition to linear instability theory we include an analysis of fully nonlinear stability theory. The theory analysed possesses a bi-Laplacian term for the velocity field and also for the temperature field. It was pointed out by E. Fried and M. Gurtin that higher order terms represent micro-length effects and these phenomena are very important in flows in microfluidic situations. We introduce temperature into the theory via a Boussinesq approximation where the density of the body force term is allowed to depend upon temperature to account for buoyancy effects which arise due to expansion of the fluid when this is heated. We analyse a meaningful set of boundary conditions which are introduced by Fried and Gurtin as conditions of strong adherence, and these are crucial to understand the effect of the higher order derivatives upon convective motion in a microfluidic scenario where micro-length effects are paramount. The basic steady state is the one of zero velocity, but in contrast to the classical theory the temperature field is nonlinear in the vertical coordinate. This requires care especially dealing with nonlinear theory and also leads to some novel effects.Comment: 20 pages, 3 tables, 4 figure

Pulmonary hypertension and chronic lung disease: where are we headed?

Pulmonary hypertension related to chronic lung disease, mainly represented by COPD and idiopathic pulmonary fibrosis, is associated with a worse outcome when compared with patients only affected by parenchymal lung disease. At present, no therapies are available to reverse or slow down the pathological process of this condition and most of the clinical trials conducted to date have had no clinically significant impact. Nevertheless, the importance of chronic lung diseases is always more widely recognised and, along with its increasing incidence, associated pulmonary hypertension is also expected to be growing in frequency and as a health burden worldwide. Therefore, it is desirable to develop useful and reliable tools to obtain an early diagnosis and to monitor and follow-up this condition, while new insights in the therapeutic approach are explored

Comorbidities in idiopathic pulmonary fibrosis: an underestimated issue

Idiopathic pulmonary fibrosis (IPF) is a progressive and fibrosing lung disease with a poor prognosis. Between 60% and 70% of IPF patients die of IPF; the remaining causes of death may be due to comorbidities occurring in this ageing population. Interest in the role played by comorbidities in IPF has increased in the past few years. The optimal clinical management of IPF is multifaceted and not only involves antifibrotic treatment, but also vaccinations, oxygen supplementation, evaluation of nutritional status as well as psychological support and patient education. Symptom management, pulmonary rehabilitation, palliative care and treatment of comorbidities represent further areas of clinical intervention. This review analyses the major comorbidities observed in IPF, focusing on those that have the greatest impact on mortality and quality of life (QoL). The identification and treatment of comorbidities may help to improve patients' health-related QoL (i.e. sleep apnoea and depression), while some comorbidities (i.e. lung cancer, cardiovascular diseases and pulmonary hypertension) influence survival. It has been outlined that gathering comorbidities data improves the prediction of survival beyond the clinical and physiological parameters of IPF

ARR screening using IDS-iSYS aldosterone and direct renin: effects of medication in essential and renovascular hypertension, Cushing's syndrome and primary aldosteronism

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Treatment Outcomes for Men with Clinical Stage II Nonseminomatous Germ Cell Tumours Treated with Primary Retroperitoneal Lymph Node Dissection: A Systematic Review

CONTEXT Guidelines recommend primary retroperitoneal lymph node dissection (RPLND) as a treatment option for tumour marker-negative stage II nonseminomatous germ cell tumour (NSGCT). OBJECTIVE To review the literature on oncological outcomes for men with stage II NSGCT treated with RPLND. EVIDENCE ACQUISITION A systematic review of studies describing clinicopathological outcomes following primary RPLND in stage II NSGCT was conducted in the MEDLINE, EMBASE, and Cochrane Database of Systematic Reviews databases according to the Preferred Reporting Items for Systematic Review and Meta-Analysis Protocols (PRISMA-P) statement. Baseline data, perioperative and postoperative parameters, and oncological outcomes were collected. EVIDENCE SYNTHESIS In total, 12 of 4387 studies were included, from which we collected data for 835 men. Among men with clinical stage II NSGCT, pathological stage II was confirmed in 615 of 790 patients (78%). Most studies administered adjuvant chemotherapy in cases with large lymph nodes, multiple affected lymph nodes, or persistently elevated tumour markers. Recurrence was observed in 12-40% of patients without adjuvant chemotherapy and 0-4% of patients who received adjuvant chemotherapy. CONCLUSIONS The literature describing RPLND in clinical stage II NSGCT is heterogeneous and no meta-analysis was possible, but RPLND can provide accurate staging and may be curative in selected patients. PATIENT SUMMARY We reviewed the literature to summarise results after surgical removal of enlarged lymph nodes in the back of the abdomen in men with testis cancer. This procedure provides accurate information on how far the cancer has spread and may provide a cure in selected patients

Notulae to the Italian alien vascular flora 6

In this contribution, new data concerning the distribution of vascular flora alien to Italy are presented. It includes new records, confirmations, exclusions, and status changes for Italy or for Italian administrative regions of taxa in the genera Acalypha, Acer, Canna, Cardamine, Cedrus, Chlorophytum, Citrus, Cyperus, Epilobium, Eucalyptus, Euphorbia, Gamochaeta, Hesperocyparis, Heteranthera, Lemna, Ligustrum, Lycium, Nassella, Nothoscordum, Oenothera, Osteospermum, Paspalum, Pontederia, Romulea, Rudbeckia, Salvia, Sesbania, Setaria, Sicyos, Styphnolobium, Symphyotrichum, and Tradescantia. Nomenclature and distribution updates, published elsewhere, and corrigenda are provided as supplementary material

Notulae to the Italian alien vascular flora: 7

In this contribution, new data concerning the distribution of vascular flora alien to Italy are presented. It includes new records, confirmations, and status changes for Italy or for Italian administrative regions of taxa in the genera Abies, Actinidia, Alooe, Amaryllis, Anredera, Arctotheca, Bidens, Cardiospermum, Celosia, Commelina, Cotoneaster, Cyclamen, Eclipta, Euphorbia, Grevillea, Hedera, Hibiscus, Impatiens, Juglans, Kalanchoe, Koelreuteria, Lindernia, Melinis, Myriophyllum, Nandina, Nicotiana, Oenothera, Oxalis, Parthenocissus, Phoenix, Phyllanthus, Physalis, Plumbago, Pteris, Quercus, Setaria, Symphytum, Tagetes, and Washingtonia. Nomenclatural and distribution updates, published elsewhere are provided as Suppl. material 1