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

First Evaluation of Dynamic Aperture at Injection for FCC-hh

In the Hadron machine option, proposed in the context of the Future Circular Colliders (FCC) study, the dipole field quality is expected to play an important role, as in the LHC. A preliminary evaluation of the field quality of dipoles, based on the Nb$_{3}$Sn technology, has been provided by the magnet group. The effect of these field imperfections on the dynamic aperture, using the present lattice design, is presented and first tolerances on the b$_3$ and b$_5$ multipole components are evaluated

How Can Molecular Pharmacology Help Understand the Multiple Actions of Melatonin: 20 Years of Research and Trends

Melatonin actions are so numerous that a naive reader might become suspicious at such wonders. In a systematic way, we would like to summarize the various approaches that led to what is scientifically sounded in terms of molecular pharmacology: where and how melatonin is acting as a molecule, what can be its action as an antioxidant per se, and its side effects at a molecular level not as a drug or in vivo. Finally, the nature of the relationship between melatonin and mitochondria should be decrypted as well. The road we took from 1987 up to now, and particularly after 1995, will be mentioned with special considerations to the receptors from various species and our goals beyond that; the synthesis and catabolism of melatonin and their link to other enzymes; the discovery of the MT3 binding sites, and what’s left to understand on this particularly interesting target; and the search for agonists that occulted part of the potential discovery of true and potent antagonists, a situation quite unique among the G-protein-coupled receptors

Coupling techniques for nonlinear hyperbolic equations. III. The well-balanced approximation of thick interfaces

We continue our analysis of the coupling between nonlinear hyperbolic problems across possibly resonant interfaces. In the first two parts of this series, we introduced a new framework for coupling problems which is based on the so-called thin interface model and uses an augmented formulation and an additional unknown for the interface location; this framework has the advantage of avoiding any explicit modeling of the interface structure. In the present paper, we pursue our investigation of the augmented formulation and we introduce a new coupling framework which is now based on the so-called thick interface model. For scalar nonlinear hyperbolic equations in one space variable, we observe that the Cauchy problem is well-posed. Then, our main achievement in the present paper is the design of a new well-balanced finite volume scheme which is adapted to the thick interface model, together with a proof of its convergence toward the unique entropy solution (for a broad class of nonlinear hyperbolic equations). Due to the presence of a possibly resonant interface, the standard technique based on a total variation estimate does not apply, and DiPerna's uniqueness theorem must be used. Following a method proposed by Coquel and LeFloch, our proof relies on discrete entropy inequalities for the coupling problem and an estimate of the discrete entropy dissipation in the proposed scheme.Comment: 21 page

China\u27s defence industries : change and continuity

Asia looks and feels very different now compared to the days of the Cold War. The sense that Asia now works differently can be traced to a single source &ndash; the re-emergence of China. China was the dominant power in greater Asia for most of recorded history. This historical norm was interrupted from the early 19th century, too far into the past to be recognisable and readily accommodated by the actors in today&rsquo;s international arena. A powerful China feels new and unfamiliar.Arriving peacefully at mutually acceptable relationships of power and influence that are very different from those that have prevailed for the past half century will be a demanding process. The world&rsquo;s track record on challenges of this kind is not terrific. It will call for statesmanship of a consistently high order from all the major players, and building the strongest possible confidence among these players that there are no hidden agendas.<br /

Development of space stable thermal control coatings for use on large space vehicles

The evaluation and environmental testing of zinc orthotitanate pigments for use as space stable thermal control coatings on large space vehicles are discussed. Electron paramagnetic resonance spectra of the pigments and their precursor compounds are examined. A continuing study of the spectral intensity of mercury-argon and mercury-xenon sources in reported. Results of long term environmental testing of commercially available, strippable, protective coatings are discussed

Wolf, Canis lupus, Pup Mortality: Interspecific Predation or Non-Parental Infanticide?

A breeding male Gray Wolf, Canis lupus, equipped with a GPS collar was documented going to the den site of another Gray Wolf pack. This trip was coincident with an attack on the den of the other pack and the occurrence of a dead and partially consumed Gray Wolf pup at the same location. We present two possible explanations - interspecific predation and non-parental infanticide - to account for this observation. Because the Gray Wolf with the GPS collar and his mate were first-time breeders and were attempting to establish a territory space of their own, we speculate that, based on the available evidence, this observation most likely represents a case of non-parental infanticide that fits the predictions of the resource competition hypothesis

Evidence of Arboreal Lichen Use in Peatlands by White-tailed Deer, Odocoileus virginianus, in Northeastern Alberta

Within the past 10 to 15 years, White-tailed Deer (Odocoileus virginianus) have extended their geographical range to include most of northern Alberta. In the boreal forest they are most abundant in well-drained upland habitat. We report the occurrence of unusually large numbers of deer seen in a large fen complex in the west side of the Athabasca River Caribou range in northeastern Alberta. Further, we report an observation that suggests that deer may be using arboreal lichen (old man&rsquo;s beard; Bryoria spp. and Usnea spp.) as a winter food in this region. We discuss the potential ecological ramifications of this observation for Woodland Caribou (Rangifer tarandus caribou) in northeastern Alberta