Structural instability of nonlinear plates modelling suspension bridges: mathematical answers to some long-standing questions

We model the roadway of a suspension bridge as a thin rectangular plate and we study in detail its oscillating modes. The plate is assumed to be hinged on its short edges and free on its long edges. Two different kinds of oscillating modes are found: longitudinal modes and torsional modes. Then we analyze a fourth order hyperbolic equation describing the dynamics of the bridge. In order to emphasize the structural behavior we consider an isolated equation with no forcing and damping. Due to the nonlinear behavior of the cables and hangers, a structural instability appears. With a finite dimensional approximation we prove that the system remains stable at low energies while numerical results show that for larger energies the system becomes unstable. We analyze the energy thresholds of instability and we show that the model allows to give answers to several questions left open by the Tacoma collapse in 1940.Comment: 33 page

On a quasilinear elliptic differential equation in unbounded domains

Existence and multiplicity results for a variational quasilinear elliptic equation on unbounded domains are proved; the solutions are obtained as critical points of a nonsmooth functional. We consider the case where the functional is coercive or has a saddle-point geometry

The evolution Navier-Stokes equations in a cube under Navier boundary conditions: rarefaction and uniqueness of global solutions

We study the evolution Navier-Stokes equations in a cube under Navier boundary conditions. For the related stationary Stokes problem, we determine explicitly all the eigenvectors, eigenvalues and the corresponding Weyl asymptotic. We introduce the notion of rarefaction, namely families of eigenvectors that weakly interact with each other through the nonlinearity. By combining the spectral analysis with rarefaction, we expand the solutions in Fourier series, making explicit some of their properties. We then suggest several new points of view in order to explain the striking difference in uniqueness results between 2D and 3D. First, we construct examples of solutions for which the nonlinearity plays a minor role, both in 2D and 3D. Second, we show that, if a solution is rarefied, then its energy is decreasing: hence, rarefaction may be seen as an almost two dimensional assumption. Finally, by exploiting the explicit form of the eigenvectors we provide a numerical explanation of the difficulty in using energy methods for general solutions of the 3D equations

Holarchical Innovation Teams: Terms & Definitions

This paper establishes the terms and definitions for the nascent discipline of Holarchical Innovation Teams (HITs). It provides a Review of Literature of those individuals who have contributed to our understanding of holarchies and who assist in creating an etymology for HITs in order to lay the foundations for subsequent papers on HITs philosophy and principles for future researchers and scholars of the disciplin

Evolução da produção e do mercado mundial do feijão.

Realizou-se uma avaliação do mercado internacional de feijão, considerando produção, exportação e importação, mostrando o comportamento e oscilações dos principais países

Weighted Sobolev spaces of radially symmetric functions

We prove dilation invariant inequalities involving radial functions, poliharmonic operators and weights that are powers of the distance from the origin. Then we discuss the existence of extremals and in some cases we compute the best constants.Comment: 38 page

Sharing Positive Affective States Amongst Rodents

Group living is thought to benefit from the ability to empathize with others. Much attention has been paid to empathy for the pain of others as an inhibitor of aggression. Empathizing with the positive affect of others has received less attention although it could promote helping by making it vicariously rewarding. Here, we review this latter, nascent literature to show that three components of the ability to empathize with positive emotions are already present in rodents, namely, the ability to perceive, share, and prefer actions that promote positive emotional states of conspecifics. While it has often been argued that empathy evolved as a motivation to care for others, we argue that these tendencies may have selfish benefits that could have stabilized their evolution: approaching others in a positive state can provide information about the source of valuable resources; becoming calmer and optimistic around animals in a calm or positive mood can help adapt to the socially sensed safety level in the environment; and preferring actions also benefiting others can optimize foraging, reduce aggression, and trigger reciprocity. Together, these findings illustrate an emerging field shedding light on the emotional world of rodents and on the biology and evolution of our ability to cooperate in groups.</p

Natural wine as an expression of sustainability: an exploratory analysis of Italy’s restaurant industry

Purpose – Although not yet fully defined, natural wine represents a sector that has gained the widespread attention of final consumers and, therefore, also of the restaurant world, because of its promise of sustainability. The objective of this paper is to understand Italian haute cuisine’s interest in natural wine, with the aim of analysing what qualifies this product as sustainable. Design/methodology/approach – After introducing a theoretical framework based on the concept of natural wine, a brief paragraph is dedicated to consumer preferences; subsequently, the analysis focusses on a questionnaire given to restaurateurs to determine the impact that natural wine has had in the Italian context. The results try to identify the importance that restaurateurs give to the characteristics of natural wine and their propensity for using such wine in their own businesses. Findings – The analysis, conducted on a sample of medium-high range restaurants, highlights their strong interest in natural wine, as a result of the final consumers’ attitude towards wine with characteristics attributable to sustainability. The positive perception by restaurateurs is similar across Italy, both geographically and in terms of the size of the restaurant. Originality/value – The originality of the work is the focus on the world of restaurants. To date, the literature on natural wine remains embryonic and always refers to the final consumer. This research is the first step in a broader study that will involve a greater number of restaurants, extending beyond Italy to all of Europe, with the aim of understanding the real development potential of natural win