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

One-loop conformal anomaly in an implicit momentum space regularization framework

In this paper we consider matter fields in a gravitational background in order to compute the breaking of the conformal current at one-loop order. Standard perturbative calculations of conformal symmetry breaking expressed by the non-zero trace of the energy-momentum tensor have shown that some violating terms are regularization dependent, which may suggest the existence of spurious breaking terms in the anomaly. Therefore, we perform the calculation in a momentum space regularization framework in which regularization dependent terms are judiciously parametrized. We compare our results with those obtained in the literature and conclude that there is an unavoidable arbitrariness in the anomalous term $\Box R$.Comment: in European Physical Journal C, 201

Conductivity of Coulomb interacting massless Dirac particles in graphene: Regularization-dependent parameters and symmetry constraints

We compute the Coulomb correction $\mathcal{C}$ to the a. c. conductivity of interacting massless Dirac particles in graphene in the collisionless limit using the polarization tensor approach in a regularization independent framework. Arbitrary parameters stemming from differences between logarithmically divergent integrals are fixed on physical grounds exploiting only spatial $O(2)$ rotational invariance of the model which amounts to transversality of the polarization tensor. Consequently $\mathcal{C}$ is unequivocally determined to be $(19- 6\pi)/12$ within this effective model. We compare our result with explicit regularizations and discuss the origin of others results for $\mathcal{C}$ found in the literature

The role of" Special Economic Zones"(SEZ) of the ICT industry for the development of the creative industry in Kazakhstan

Nowadays, the creative industry in Kazakhstan is a young direction of the economy. The government supports this industry with tax benefits, the provision of infrastructure, as well as the creation of Special Economic Zones (SEZ) in large megacities of the country like Nur-Sultan (Astana) and Almaty. "Astana Hub” and the park of innovative technologies “Alatau" are the main centers of development of the organization of the ICT industry as cluster formations. In this paper, an overview study was conducted to determine the role of these SEZs for the development of the creative industry in Kazakhstan. Firstly, the concept of the creative industry was considered, then a literary review of the creative industry and special economic zones was conducted, and thirdly, a review was made on special economic zones that contribute to the development of the creative industry in Kazakhsta

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

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

Design and modeling of a periodic single-phase sandwich panel for acoustic insulation applications

Sandwich and composite panels are widely adopted in acoustic applications due to their sound insulation properties that overcome mass-law-based partitions in medium–high frequency regions. A key aspect in the design procedure of acoustic panels is the control of the resonance-dominated region of the sound transmission loss (STL) curve. Within that frequency range, such systems usually show acoustic weakness and poor insulation performances with respect to standard single-layer solutions. In the present contribution, we want to highlight an innovative approach to the sandwich partition concept. A novel single-phase sandwich panel is realized by adopting a periodic repetition of a properly designed unit cell. The resulting internal truss structure is self-sustained, and its mechanical stiffness can be tuned to maximize the STL in the resonance-dominated region. A set of parametric analyses is reported to show how the topology of the unit cell affects the noise reduction properties of the panel. Experimental validation is performed on a nylon 3D-printed prototype. The proposed panel is then integrated with some locally resonant elements that can be adopted to further improve the low-frequency STL of the solution. Industrial and production considerations are also taken into account during the design process to make the solution industrially valid with a circular economy focus

Brazil nut almonds: nutritional and market aspects.

The aim of this study was to estimate the annual growth rate in production and exportation of Brazil nut almonds. Presents information related to the composition of different fatty acids from brazil nut almonds and the human daily intake needs, as well as an analysis of its production, its growth rate during the last 20 years and its export. and the human daily intake needs

Consumo, valor nutritivo e evolução da produção e de mercado mundial de feijão.

Apresentado Painel na 6º Semana de Ensino, Pesquisa e Extensão Universidade Federal de Santa Catarina