Discrete Dynamical Systems: A Brief Survey

Dynamical system is a mathematical formalization for any fixed rule that is described in time dependent fashion. The time can be measured by either of the number systems - integers, real numbers, complex numbers. A discrete dynamical system is a dynamical system whose state evolves over a state space in discrete time steps according to a fixed rule. This brief survey paper is concerned with the part of the work done by José Sousa Ramos [2] and some of his research students. We present the general theory of discrete dynamical systems and present results from applications to geometry, graph theory and synchronization

The q-gradient method for global optimization

The q-gradient is an extension of the classical gradient vector based on the concept of Jackson's derivative. Here we introduce a preliminary version of the q-gradient method for unconstrained global optimization. The main idea behind our approach is the use of the negative of the q-gradient of the objective function as the search direction. In this sense, the method here proposed is a generalization of the well-known steepest descent method. The use of Jackson's derivative has shown to be an effective mechanism for escaping from local minima. The q-gradient method is complemented with strategies to generate the parameter q and to compute the step length in a way that the search process gradually shifts from global in the beginning to almost local search in the end. For testing this new approach, we considered six commonly used test functions and compared our results with three Genetic Algorithms (GAs) considered effective in optimizing multidimensional unimodal and multimodal functions. For the multimodal test functions, the q-gradient method outperformed the GAs, reaching the minimum with a better accuracy and with less function evaluations.Comment: 12 pages, 1 figur

Brittle fracture of polymer transient networks

We study the fracture of reversible double transient networks, constituted of water suspensions of entangled surfactant wormlike micelles reversibly linked by various amounts of telechelic polymers. We provide a state diagram that delineates the regime of fracture without necking of the filament from the regime where no fracture or break-up has been observed. We show that filaments fracture when stretched at a rate larger than the inverse of the slowest relaxation time of the networks. We quantitatively demonstrate that dissipation processes are not relevant in our experimental conditions and that, depending on the density of nodes in the networks, fracture occurs in the linear viscoelastic regime or in a non-linear regime. In addition, analysis of the crack opening profiles indicates deviations from a parabolic shape close to the crack tip for weakly connected networks. We demonstrate a direct correlation between the amplitude of the deviation from the parabolic shape and the amount of non linear viscoelasticity

Avaliação do potencial da madeira de Eucalyptus urograndis para a produção de etanol celulósico a partir do pré-tratamento por explosão a vapor e hidrólise enzimática.

Resumo

Avaliação do potencial da madeira de Eucalyptus urograndis para a produção de etanol celulósico a partir do pré-tratamento por explosão vapor e hidrólise enzimática.

Resumo