31,589 research outputs found
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
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