Genus zero transverse foliations for weakly convex Reeb flows on the tight 33-sphere

A contact form on the tight $3$-sphere $(S^3,\xi_0)$ is called weakly convex if the Conley-Zehnder index of every Reeb orbit is at least $2$. In this article, we study Reeb flows of weakly convex contact forms on $(S^3,\xi_0)$ admitting a prescribed finite set of index-$2$ Reeb orbits, which are all hyperbolic and mutually unlinked. We present conditions so that these index-$2$ orbits are binding orbits of a genus zero transverse foliation whose additional binding orbits have index $3$. In addition, we show in the real-analytic case that the topological entropy of the Reeb flow is positive if the branches of the stable/unstable manifolds of the index-$2$ orbits are mutually non-coincident.Comment: 47 pages; The main results remain unchange

Experi?ncia de economia solid?ria: um estudo de caso sobre a Associa??o dos Catadores de Materiais Recicl?veis de Diamantina

O presente trabalho tem como objetivo analisar o funcionamento de uma experi?ncia de gera??o de renda inspirada nos princ?pios da economia solid?ria, a saber, as atividades produtivas da Associa??o dos Catadores de Materiais Recicl?veis de Diamantina (ACAD). Para realizar o estudo de caso sobre a ACAD, a metodologia utilizada nesta pesquisa consistiu em um levantamento bibliogr?fico, jur?dico e documental sobre diversos temas e problemas relativos a esse tipo de experi?ncia. Em primeiro lugar, foram analisadas quest?es centrais referentes aos princ?pios da economia solid?ria, seus objetivos e problemas, assim como o trabalho dos catadores de materiais recicl?veis. Posteriormente, foi realizado um levantamento a respeito das pol?ticas p?blicas de res?duos s?lidos em n?vel nacional, estadual e municipal. No ?ltimo cap?tulo, foi realizado um estudo sobre os documentos e sobre parte do cotidiano da referida associa??o observado durante a participa??o em um projeto de extens?o, com o objetivo de compreender seu funcionamento, suas caracter?sticas, seus desafios e suas rela??es com o poder p?blico local. Verificou-se, por fim, que a ACAD tem apresentado dificuldades para manter seu funcionamento de acordo com os princ?pios da economia solid?ria e para se manter de forma aut?noma em rela??o ? Prefeitura Municipal de Diamantina.Disserta??o (Mestrado Profissional) ? Programa de P?s-Gradua??o em Ci?ncias Humanas, Universidade Federal dos Vales do Jequitinhonha e Mucuri, 2018.The present work aims to analyze the functioning of an income generation experience inspired by the principles of solidarity economy, namely, the productive activities of the Association of Collectors of Recyclable Materials of Diamantina (ACAD). In order to carry out the case study on ACAD, the methodology used in this research consisted of a bibliographic, legal and documentary survey on various themes and problems related to this type of experience. Firstly, central issues were discussed concerning the principles of solidarity economy, its objectives and problems, as well as the work of collectors of recyclable materials. Subsequently, a survey was carried out on the public policies of solid waste at national, state and municipal levels. In the last chapter, a study was carried out on the documents and part of the quotidian of this association observed during the participation in an extension project, with the objective of understanding it?s functioning, its characteristics, its challenges and its relations with local public power. Finally, it was verified that ACAD has presented difficulties to maintain its operation in accordance with the principles of the solidarity economy and to maintain itself autonomously in relation to the Municipality of Diamantina

Analytical model for the prediction of permeability of triply periodic minimal surfaces

Triply periodic minimal surfaces (TPMS) are mathematically defined cellular structures whose geometry can be quickly adapted to target desired mechanical response (structural and fluid). This has made them desirable for a wide range of bioengineering applications; especially as bioinspired materials for bone replacement. The main objective of this study was to develop a novel analytical framework which would enable calculating permeability of TPMS structures based on the desired architecture, pore size and porosity. To achieve this, computer-aided designs of three TPMS structures (Fisher-Koch S, Gyroid and Schwarz P) were generated with varying cell size and porosity levels. Computational Fluid Dynamics (CFD) was used to calculate permeability for all models under laminar flow conditions. Permeability values were then used to fit an analytical model dependent on geometry parameters only. Results showed that permeability of the three architectures increased with porosity at different rates, highlighting the importance of pore distribution and architecture. The computed values of permeability fitted well with the suggested analytical model (R2>0.99, p<0.001). In conclusion, the novel analytical framework presented in the current study enables predicting permeability values of TPMS structures based on geometrical parameters within a difference <5%. This model, which could be combined with existing structural analytical models, could open new possibilities for the smart optimisation of TPMS structures for biomedical applications where structural and fluid flow properties need to be optimised

Additively manufactured lattice structures with controlled transverse isotropy for orthopedic porous implants

Additively manufactured lattice structures enable the design of tissue scaffolds with tailored mechanical properties, which can be implemented in porous biomaterials. The adaptation of bone to physiological loads results in anisotropic bone tissue properties which are optimized for site-specific loads; therefore, some bone sites are stiffer and stronger along the principal load direction compared to other orientations. In this work, a semi-analytical model was developed for the design of transversely isotropic lattice structures that can mimic the anisotropy characteristics of different types of bone tissue. Several design possibilities were explored, and a particular unit cell, which was best suited for additive manufacturing was further analyzed. The design of the unit cell was parameterized and in-silico analysis was performed via Finite Element Analysis. The structures were manufactured additively in metal and tested under compressive loads in different orientations. Finite element analysis showed good correlation with the semi-analytical model, especially for elastic constants with low relative densities. The anisotropy measured experimentally showed a variable accuracy, highlighting the deviations from designs to additively manufactured parts. Overall, the proposed model enables to exploit the anisotropy of lattice structures to design lighter scaffolds with higher porosity and increased permeability by aligning the scaffold with the principal direction of the load

Meeting high precision requirements of additively manufactured components through hybrid manufacturing

A hybrid approach combining the laser powder bed fusion (LPBF) process and post-processing operations through 5-axis milling was employed to manufacture a Ti6Al4V aerospace component. From the design step, the requirements and needs in all the stages of the Hybrid Additive Manufacturing process were taken into account. A numerical simulation of distortions promoted by residual stresses during the additive process was employed to consider material allowance. The status of the as-built and post-processed component was analysed through scanning and CMM inspection and roughness measurements. The 3D scanned model of the as-built LPBF-ed component was used to understand the distortion behaviour of the component and compared to the numerical simulation. Finally, 5-axis milling operations were conducted in some critical surfaces in order to improve surface quality and dimensional accuracy of the as-built com- ponent. The inspection of the as-built and post-processed component showed the improvement achieved through the proposed hybrid approach. The work aims to provide the baselines needed to enable the metal Hybrid Additive Manufacturing of components with complex geometries where mandatory precision is required by integrating high accuracy machining operations as post-processing technique