Linear Pantographic Sheets: Existence and Uniqueness of Weak Solutions

The well-posedness of the boundary value problems for second gradient elasticity has been studied under the assumption of strong ellipticity of the dependence on the second placement gradients (see, e.g., Chambon and Moullet in Comput. Methods Appl. Mech. Eng. 193:2771–2796, 2004 and Mareno and Healey in SIAM J. Math. Anal. 38:103–115, 2006). The study of the equilibrium of planar pantographic lattices has been approached in two different ways: in dell’Isola et al. (Proc. R. Soc. Lond. Ser. A 472:20150, 2016) a discrete model was introduced involving extensional and rotational springs which is also valid in large deformations regimes while in Boutin et al. (Math. Mech. Complex Syst. 5:127–162, 2017) the lattice has been modelled as a set of beam elements interconnected by internal pivots, but the analysis was restricted to the linear case. In both papers a homogenized second gradient deformation energy, quadratic in the neighbourhood of non deformed configuration, is obtained via perturbative methods and the predictions obtained with the obtained continuum model are successfully compared with experiments. This energy is not strongly elliptic in its dependence on second gradients. We consider in this paper also the important particular case of pantographic lattices whose first gradient energy does not depend on shear deformation: this could be considered either a pathological case or an important exceptional case (see Stillwell et al. in Am. Math. Mon. 105:850–858, 1998 and Turro in Angew. Chem., Int. Ed. Engl. 39:2255–2259, 2000). In both cases we believe that such a particular case deserves some attention because of what we can understand by studying it (see Dyson in Science 200:677–678, 1978). This circumstance motivates the present paper, where we address the well-posedness of the planar linearized equilibrium problem for homogenized pantographic lattices. To do so: (i) we introduce a class of subsets of anisotropic Sobolev’s space as the most suitable energy space E relative to assigned boundary conditions; (ii) we prove that the considered strain energy density is coercive and positive definite in E; (iii) we prove that the set of placements for which the strain energy is vanishing (the so-called floppy modes) must strictly include rigid motions; (iv) we determine the restrictions on displacement boundary conditions which assure existence and uniqueness of linear static problems. The presented results represent one of the first mechanical applications of the concept of Anisotropic Sobolev space, initially introduced only on the basis of purely abstract mathematical considerations

Deformation of an elastic second gradient spherical body under equatorial line density of dead forces

We consider deformations of an elastic body having initially a spherical shape. Assumed deformation energy depends on the first and second gradient of displacements. We apply an equatorial line density of dead loads, that are forces per unit line length directed in radial direction and applied along the equator of the sphere. We restrict ourselves our analysis to the case of linearized second strain gradient isotropic elasticity (for which the more general energy was determined by Mindlin) with only one characteristic length. Differently to what happens in first gradient continua, i.e. in classic linear elasticity, we show that for the particular class second gradient continua considered here these forces do not determine infinite displacements in the direction of applied dead line forces. Instead, using a series method for the solution of the considered boundary-value problem, we demonstrate that the displacements are finite. So in the deformed configuration there is not the formation of an edge at the material points where the forces are applied. Further investigations are therefore needed for establishing if this elastic-regime edge formation is made possible: (I) either in the case of more general linear elastic constitutive equations or (II) only when large deformations are considered or (III) if non-elastic phenomena are involved

Individual metering and submetering for cooling application

In 2012 the Energy Efficiency Directive (EED) has set mandatory installation of individual metering and submetering systems for accounting thermal energy consumption in buildings where centralized heating/cooling sources are present, when technically feasible and cost efficient. As a consequence, direct thermal energy meters or indirect heat accounting systems have spread widely in residential buildings, for metering and sub-metering in space heating applications. On the other hand, individual metering of thermal energy in space cooling is a difficult task, due to the very different types of cooling systems and to the lack of technical and legal metrology regulation. In this paper possible solutions available for direct metering and submetering of different types of centralized cooling systems are discussed. Indeed, for direct metering application, the cooling fluid flow metering is a particularly crucial issue due to small pipe diameters and different fluid properties. Thus, the authors carried out an experimental comparison between a Coriolis flow-meter and an ultrasonic clamp-on flow-meter in the cooling fluid circuit of a direct expansion system. Tests have been performed at different operative temperature differences between flow and return, showing relative errors within ± 10%

Classification of patients with knee osteoarthritis in clinical phenotypes: data from the osteoarthritis initiative

<div><p>Objectives</p><p>The existence of phenotypes has been hypothesized to explain the large heterogeneity characterizing the knee osteoarthritis. In a previous systematic review of the literature, six main phenotypes were identified: Minimal Joint Disease (MJD), Malaligned Biomechanical (MB), Chronic Pain (CP), Inflammatory (I), Metabolic Syndrome (MS) and Bone and Cartilage Metabolism (BCM). The purpose of this study was to classify a sample of individuals with knee osteoarthritis (KOA) into pre-defined groups characterized by specific variables that can be linked to different disease mechanisms, and compare these phenotypes for demographic and health outcomes.</p><p>Methods</p><p>599 patients were selected from the OAI database FNIH at 24 months’ time to conduct the study. For each phenotype, cut offs of key variables were identified matching the results from previous studies in the field and the data available for the sample. The selection process consisted of 3 steps. At the end of each step, the subjects classified were excluded from the further classification stages. Patients meeting the criteria for more than one phenotype were classified separately into a ‘complex KOA’ group.</p><p>Results</p><p>Phenotype allocation (including complex KOA) was successful for 84% of cases with an overlap of 20%. Disease duration was shorter in the MJD while the CP phenotype included a larger number of Women (81%). A significant effect of phenotypes on WOMAC pain (F = 16.736 p <0.001) and WOMAC physical function (F = 14.676, p < 0.001) was identified after controlling for disease duration.</p><p>Conclusion</p><p>This study signifies the feasibility of a classification of KOA subjects in distinct phenotypes based on subgroup-specific characteristics.</p></div

Derivation of dual horizon state-based peridynamics formulation based on euler-lagrange equation

The numerical solution of peridynamics equations is usually done by using uniform spatial discretisation. Although implementation of uniform discretisation is straightforward, it can increase computational time significantly for certain problems. Instead, non-uniform discretisation can be utilised and different discretisation sizes can be used at different parts of the solution domain. Moreover, the peridynamic length scale parameter, horizon, can also vary throughout the solution domain. Such a scenario requires extra attention since conservation laws must be satisfied. To deal with these issues, dual-horizon peridynamics was introduced so that both non-uniform discretisation and variable horizon sizes can be utilised. In this study, dual-horizon peridynamics formulation is derived by using Euler–Lagrange equation for state-based peridynamics. Moreover, application of boundary conditions and determination of surface correction factors are also explained. Finally, the current formulation is verified by considering two benchmark problems including plate under tension and vibration of a plate

Synthesis and antiviral activity of novel spirocyclic nucleosides

The synthesis of a number of spirocyclic ribonucleosides containing either a triazolic or azetidinic system is described, along with two analogous phosphonate derivatives of the former. These systems were constructed from the same β-D-psicofuranose starting material. The triazole spirocyclic nucleosides were constructed using the 1-azido-1-hydroxymethyl derived sugars, where the primary alcohol was alkylated with a range of propargyl bromides, whereas the azetidine systems orginated from the corresponding 1-cyano-1-hydroxymethyl sugars. Owing to their close similarity with ribavirin, the library of compounds were investigated for their antiviral properties using MHV (Murine Hepatitis Virus) as a model

Stress da radiazione RF a 900 MHz ed attivazione di elementi trasponibili in tessuti germinali di Drosophila melanogaster

Nel mondo naturale gli individui, le popolazioni e le specie si devono confrontare con variazioni delle condizioni ambientali. Gli organismi e le loro cellule mettono in atto un adattamento fisiologico attraverso risposte che sono immediate e reversibili. Condizioni di stress però, possono causare modificazioni a livello genomico che possono alterare processi biologici fondamentali conducendo a trasformazioni cellulari. È noto da tempo che fattori ambientali provocano condizioni di stress che possono indurre in vari organismi l’attivazione di elementi genetici mobili o elementi trasponibili (TEs) il cui movimento è tra le cause di instabilità genomica. In questo lavoro, individui di Drosophila melanogaster sono stati sottoposti a stress da radiazione RF a 900 MHz ed esaminati per l’attivazione di TEs nei tessuti germinali di entrambi i sessi. Tale stress ha causato un significativo incremento dell’attivazione di tali elementi, confermando che diversi stress ambientali possono avere come conseguenza l’instabilità dei genomi e la comparsa di mutazioni de novo dovute all’inserzione di elementi trasponibili in geni codificanti

A new approach for the limit to tree height using a liquid nanolayer model

Liquids in contact with solids are submitted to intermolecular forces inferring density gradients at the walls. The van der Waals forces make liquid heterogeneous, the stress tensor is not any more spherical as in homogeneous bulks and it is possible to obtain stable thin liquid films wetting vertical walls up to altitudes that incompressible fluid models are not forecasting. Application to micro tubes of xylem enables to understand why the ascent of sap is possible for very high trees like sequoias or giant eucalyptus.Comment: In the conclusion is a complementary comment to the Continuum Mechanics and Thermodynamics paper. 21 pages, 4 figures. Continuum Mechanics and Thermodynamics 20, 5 (2008) to appea