An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds

For a given self-map f of M, a closed smooth connected and simply-connected manifold of dimension m ≥ 4, we provide an algorithm for estimating the values of the topological invariant Dm r [f], which equals the minimal number of r-periodic points in the smooth homotopy class of f. Our results are based on the combinatorial scheme for computing Dm r [f] introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63–84]. An open-source implementation of the algorithm programmed in C++ is publicly available at http://www.pawelpilarczyk.com/combtop/.

Structure-property relationships in polymer nanocomposites

Tese de Doutoramento em Ciência e Engenharia de Polímeros e Compósitos

Dispersion of fillers in viscoelastic polymer matrices using Eulerian-Lagrangian approaches

Understanding the behavior of c omplex composite materials using mixing procedures is fundamental in several industrial processes. For instance, polymer composites are usually manufactured using dispersion of fillers in polymer melt matrices. The success of the filler dispersion depends both on the complex flow patterns generated and on the polymer melt rheological behavior. Consequently, the availability of a numerical tool that allow to model both fluid and particle would be very useful to increase the process insight. Nowadays there ar e computational tools that allow modeling the behavior of filled systems, taking into account both the behavior of the fluid (Computational Rheology) and the particles (Discrete Element Method). One example is the DPMFoam solver of the OpenFOAM ® framework where the averaged volume fraction momentum and mass conservation equations are used to describe the fluid (continuous phase) rheology, and the Newton’s second law of motion is used to compute the particles (discrete phase) movement. In this work the refer red solver is extended to take into account the elasticity of the polymer melts for the continuous phase. The solver capabilities will be illustrated by studying the effect of the fluid rheology on the filler dispersion, taking into account different fluid types (generalized Newtonian or viscoelastic) and particles volume fraction and size. The results obtained are used to evaluate the relevance of considering the fluid complex rheology for the prediction of the composites morphology

Low f-number microlenses for integration on optical microsystems

This paper presents microlenses (MLs) with low f-number made of AZ4562 photoresist for integration on optical microsystems. The fabrication process was based on the thermal reflow and rehydration. Large series of MLs were fabricated with a width of 35 μm, a thickness of 5 μm, and spaced apart by 3 μm. The MLs were fabricated directly on the surface of a die with type n+/p-substrate junction photodiode fabricated in a standard CMOS process. The measured focal length was 49 μm with a tolerance of ±2 μm (maximum error of ±4%), resulting in a numerical aperture of 33.6 × 10-2 (±1.3 × 10-2). The measurements also revealed an f-number of 1.4.

Conflito e trauma: XVI Colóquio de Outono

It has been the main concern of CEHUM, as a Research Centre within the Humanities which operates in an inter and transdisciplinary structure to listen attentively to the “noise of the world” and attempt a global interpretation of the signs of the times issuing from the world around us, as vibrant echoes of many social and cultural pressing issues. Every year each new Colóquio de Outono attempts to give evidence of that concern through the topic chosen for debate, ample enough and challenging enough to trigger a lively multidisciplinary dialogue amongst the diff erent research groups that compose this centre, the participants and our invited guest speakers. Throughout the three days of this 16th Colóquio de Outono we had the privilege to debate the propositions of a vast number of national and international specialists in the manifold fi elds of inquiry here represented, engaging keynote speakers, project advisors, members of research teams and external researchers attached to the various research projects currently running in CEHUM, in the fi elds of literature, linguistics, philosophy, ethics, visual arts, cultural studies, music and performance. Each specifi c fi eld of studies was however never seen isolated, but always embodied in a geo-cultural context and within the scope of a wide variety of critical debates and current theories of knowledge, as a signal of our understanding of the Humanities as a rich and plural territory which engages us all, scholars, researchers, students.

Euler angles, Bryant angles and Euler parameters

This chapter deals with the different approaches for describing the rotational coordinates in spatial multibody systems. In this process, Euler angles and Bryant angles are briefly characterized. Particular emphasis is given to Euler parameters, which are utilized to describe the rotational coordinates in the present work. In addition, for all the types of coordinates considered in this chapter, a characterization of the transformation matrix is fully described.