On a generalized Laguerre operational matrix of fractional integration

A new operationalmatrix of fractional integration of arbitrary order for generalized Laguerre polynomials is derived.The fractional integration is described in the Riemann-Liouville sense.This operational matrix is applied together with generalized Laguerre tau method for solving general linearmultitermfractional differential equations (FDEs).Themethod has the advantage of obtaining the solution in terms of the generalized Laguerre parameter. In addition, only a small dimension of generalized Laguerre operational matrix is needed to obtain a satisfactory result. Illustrative examples reveal that the proposedmethod is very effective and convenient for linear multiterm FDEs on a semi-infinite interval.

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

Complex evolution of a multi-particle system

This paper studies a discrete dynamical system of interacting particles that evolve by interacting among them. The computational model is an abstraction of the natural world, and real systems can range from the huge cosmological scale down to the scale of biological cell, or even molecules. Different conditions for the system evolution are tested. The emerging patterns are analysed by means of fractal dimension and entropy measures. It is observed that the population of particles evolves towards geometrical objects with a fractal nature. Moreover, the time signature of the entropy can be interpreted at the light of complex dynamical systems.

A case study on the improvement of eco-efficiency ratios: application to a composite processing industry

The World Business Council for Sustainable Development (WBCSD) defines Eco-Efficiency as follows: ‘Eco- Efficiency is achieved by the delivery of competitively priced-goods and services that satisfy human needs and bring quality of life, while progressively reducing ecological impacts and resource intensity throughout the life-cycle to a level at least in line with the earth’s estimated carrying capacity’. Eco-Efficiency is under this point of view a key concept for sustainable development, bringing together economic and ecological progress. Measuring the Eco-Efficiency of a company, factory or business, is a complex process that involves the measurement and control of several and relevant parameters or indicators, globally applied to all companies in general, or specific according to the nature and specificities of the business itself. In this study, an attempt was made in order to measure and evaluate the eco-efficiency of a pultruded composite processing company. For this purpose the recommendations of WBCSD [1] and the directives of ISO 14301 standard [2] were followed and applied. The analysis was restricted to the main business branch of the company: the production and sale of standard GFRP pultrusion profiles. The main general indicators of eco-efficiency, as well as the specific indicators, were defined and determined according to ISO 14031 recommendations. With basis on indicators’ figures, the value profile, the environmental profile, and the pertinent eco-efficiency’s ratios were established and analyzed. In order to evaluate potential improvements on company eco-performance, new indicators values and ecoefficiency ratios were estimated taking into account the implementation of new proceedings and procedures, both in upstream and downstream of the production process, namely: a) Adoption of new heating system for pultrusion die in the manufacturing process, more effective and with minor heat losses; b) Implementation of new software for stock management (raw materials and final products) that minimize production failures and delivery delays to final consumer; c) Recycling approach, with partial waste reuse of scrap material derived from manufacturing, cutting and assembly processes of GFRP profiles. In particular, the last approach seems to significantly improve the eco-efficient performance of the company. Currently, by-products and wastes generated in the manufacturing process of GFRP profiles are landfilled, with supplementary added costs to this company traduced by transport of scrap, landfill taxes and required test analysis to waste materials. However, mechanical recycling of GFRP waste materials, with reduction to powdered and fibrous particulates, constitutes a recycling process that can be easily attained on heavy-duty cutting mills. The posterior reuse of obtained recyclates, either into a close-looping process, as filler replacement of resin matrix of GFRP profiles, or as reinforcement of other composite materials produced by the company, will drive to both costs reduction in raw materials and landfill process, and minimization of waste landfill. These features lead to significant improvements on the sequent assessed eco-efficiency ratios of the present case study, yielding to a more sustainable product and manufacturing process of pultruded GFRP profiles.