Fractional order modelling of zero length column desorption response for adsorbents with variable particle sizes

This manuscript analyses the data generated by a Zero Length Column (ZLC) diffusion experimental set-up, for 1,3 Di-isopropyl benzene in a 100% alumina matrix with variable particle size. The time evolution of the phenomena resembles those of fractional order systems, namely those with a fast initial transient followed by long and slow tails. The experimental measurements are best fitted with the Harris model revealing a power law behavior.

Fractional order modelling of fractional-order holds

Discrete time control systems require sample- and-hold circuits to perform the conversion from digital to analog. Fractional-Order Holds (FROHs) are an interpolation between the classical zero and first order holds and can be tuned to produce better system performance. However, the model of the FROH is somewhat hermetic and the design of the system becomes unnecessarily complicated. This paper addresses the modelling of the FROHs using the concepts of Fractional Calculus (FC). For this purpose, two simple fractional-order approximations are proposed whose parameters are estimated by a genetic algorithm. The results are simple to interpret, demonstrating that FC is a useful tool for the analysis of these devices.

Dynamical modelling of a genetic algorithm

This work addresses the signal propagation and the fractional-order dynamics during the evolution of a genetic algorithm (GA). In order to investigate the phenomena involved in the GA population evolution, the mutation is exposed to excitation perturbations during some generations and the corresponding fitness variations are evaluated. Three distinct fitness functions are used to study their influence in the GA dynamics. The input and output signals are studied revealing a fractional-order dynamic evolution, characteristic of a long-term system memory.

Fuzzy modelling of prescribed burning effects on soil physical properties

This paper presents the preliminary work of an approach where Fuzzy Boolean Nets (FBN) are being used to extract qualitative knowledge regarding the effect of prescribed fire burning on soil chemical physical properties. FBN were chosen due to the scarcity on available quantitative data.

Dispersion Modelling of Natural Radionuclides 238U, 232Th and 40K Released from Coal-fired Power Plants Operations

The aim of this work was to simulate the radionuclides dispersion in the surrounding area of a coal-fired power plant, operational during the last 25 years. The dispersion of natural radionuclides (236Ra, 232Th and 40K) was simulated by a Gaussian plume dispersion model with three different stability classes estimating the radionuclides concentration at ground level. Measurements of the environmen-tal activity concentrations were carried out by γ-spectrometry and compared with results from the air dispersion and deposition model which showed that the stabil-ity class D causes the dispersion to longer distances up to 20 km from the stacks.

Fractional order modelling of dynamic backlash

This paper studies the dynamical properties of systems with backlash and impact phenomena. This type of non-linearity can be tackled in the perspective of the fractional calculus theory. Fractional and integer order models are compared and their influence upon the emerging dynamics is analysed. It is demonstrated that fractional models can memorize dynamical effects due to multiple micro-collisions.

Pseudo Phase Plane and Fractional Calculus Modelling of Western Global Economic Downturn

This paper applies Pseudo Phase Plane (PPP) and Fractional Calculus (FC) mathematical tools for modeling world economies. A challenging global rivalry among the largest international economies began in the early 1970s, when the post-war prosperity declined. It went on, up to now. If some worrying threatens may exist actually in terms of possible ambitious military aggression, invasion, or hegemony, countries’ PPP relative positions can tell something on the current global peaceful equilibrium. A global political downturn of the USA on global hegemony in favor of Asian partners is possible, but can still be not accomplished in the next decades. If the 1973 oil chock has represented the beginning of a long-run recession, the PPP analysis of the last four decades (1972–2012) does not conclude for other partners’ global dominance (Russian, Brazil, Japan, and Germany) in reaching high degrees of similarity with the most developed world countries. The synergies of the proposed mathematical tools lead to a better understanding of the dynamics underlying world economies and point towards the estimation of future states based on the memory of each time series.

A Fractional Perspective to the Bond Graph Modelling of World Economies

Inspired in dynamic systems theory and Brewer’s contributions to apply it to economics, this paper establishes a bond graph model. Two main variables, a set of inter-connectivities based on nodes and links (bonds) and a fractional order dynamical perspective, prove to be a good macro-economic representation of countries’ potential performance in nowadays globalization. The estimations based on time series for 50 countries throughout the last 50 decades confirm the accuracy of the model and the importance of scale for economic performance.