A symbolic approach to nonlinearly perturbed heat equation

We consider a system described by the linear heat equation with adiabatic boundary conditions which is perturbed periodicaly. This perturbation is nonlinear and is characterized by a one-parameter family of quadratic maps. The system, depending on the parameters, presents very complex behaviour. We introduce a symbolic framework to analyze the system and resume its most important features.

Mathematics and fiber arts

Mathematics can be found all over the world, even in what could be considered an unrelated area, like fiber arts. In knitting, crochet, and counted-thread embroidery, we can find concepts of algebra, graph theory, number theory, geometry of transformations, and symmetry, as well as computer science. For example, many fiber art pieces embody notions related with groups of symmetry. In this work, we focus on two areas of Mathematics associated with knitting, crochet, and cross-stitch works – number theory and geometry of transformations.

Symbolic dynamics generated by a hybrid chaotic systems

We consider piecewise defined differential dynamical systems which can be analysed through symbolic dynamics and transition matrices. We have a continuous regime, where the time flow is characterized by an ordinary differential equation (ODE) which has explicit solutions, and the singular regime, where the time flow is characterized by an appropriate transformation. The symbolic codification is given through the association of a symbol for each distinct regular system and singular system. The transition matrices are then determined as linear approximations to the symbolic dynamics. We analyse the dependence on initial conditions, parameter variation and the occurrence of global strange attractors.

Influência de polímeros superabsorventes na retracção de argamassas

Hoje em dia, o desenvolvimento dos superplastificantes permite a produção de betões com menor razão água/cimento. Ao usar razões água/cimento mais baixas, os materiais científicos apresentam maior tendência para fissurar devido à retracção autogénea. Este trabalho apresenta um estudo sobre a utilização de polímeros superabsorventes (SAP) no controlo da retracção. O uso de SAPs em materiais comentícios atenua a retracção autogénea pois estes produtos permitem o fornecimento interno de água. Estes produtos podem também afectar outras propriedades, afectando as características mecânicas e a trabalhabilidade. Para análise do efeito dos SAP foram estudadas argamassas com várias concentrações deste produto, tendo como referência argamassas semelhantes sem SAP, determinando-se as retracções autogénea e total, a resistência à compressão e o módulo de elasticidade. Além de SAP, foi também utilizado um agregado leve, um outro tipo de introdutor de água, para comparação com os polímeros em estudo. /ABSTRACT: This work presents a study on the use of superabsorbent polymers (SAP) in the control of shrinkage. The use of SAPs in cementitious materials reduces the autogenous shrinkage because these products enable the internal supply of water. These materials can also affect other properties such as mechanical properties and workability. To analyze the effect of SAP, mortars containing various concentrations of this product were studied, in comparison with reference mortars without SAP. The tests performed were autogenous and total shrinkage, compressive strength and modulus of elasticity. Besides SAP, it was also used a lightweight aggregate, another type of internal supply of water, for comparison with the polymers under study.