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.

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.

A simple approach to numerical modelling of propane combustion in fluidized beds

A mathematical model is proposed for the evolution of temperature, chemical composition, and energy release in bubbles, clouds, and emulsion phase during combustion of gaseous premixtures of air and propane in a bubbling fluidized bed. The analysis begins as the bubbles are formed at the orifices of the distributor, until they explode inside the bed or emerge at the free surface of the bed. The model also considers the freeboard region of the fluidized bed until the propane is thoroughly burned. It is essentially built upon the quasi-global mechanism of Hautman et al. (1981) and the mass and heat transfer equations from the two-phase model of Davidson and Harrison (1963). The focus is not on a new modeling approach, but on combining the classical models of the kinetics and other diffusional aspects to obtain a better insight into the events occurring inside a fluidized bed reactor. Experimental data are obtained to validate the model by testing the combustion of commercial propane, in a laboratory-scale fluidized bed, using four sand particle sizes: 400–500, 315–400, 250–315, and 200–250 µm. The mole fractions of CO2, CO, and O2 in the flue gases and the temperature of the fluidized bed are measured and compared with the numerical results.

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 dynamics of genetic algorithms using hexagonal space tessellation

The paper formulates a genetic algorithm that evolves two types of objects in a plane. The fitness function promotes a relationship between the objects that is optimal when some kind of interface between them occurs. Furthermore, the algorithm adopts an hexagonal tessellation of the two-dimensional space for promoting an efficient method of the neighbour modelling. The genetic algorithm produces special patterns with resemblances to those revealed in percolation phenomena or in the symbiosis found in lichens. Besides the analysis of the spacial layout, a modelling of the time evolution is performed by adopting a distance measure and the modelling in the Fourier domain in the perspective of fractional calculus. The results reveal a consistent, and easy to interpret, set of model parameters for distinct operating conditions.

Modelling and segmentation of the vocal tract during speech production by using deformable models in magnetic resonance images

The first and second authors would like to thank the support of the PhD grants with references SFRH/BD/28817/2006 and SFRH/PROTEC/49517/2009, respectively, from Fundação para a Ciência e Tecnol ogia (FCT). This work was partially done in the scope of the project “Methodologies to Analyze Organs from Complex Medical Images – Applications to Fema le Pelvic Cavity”, wi th reference PTDC/EEA- CRO/103320/2008, financially supported by FCT.

Development of procedures for the simulation of atmospheric flows over complex terrain, using OpenFOAM

The main purpose of this work was the development of procedures for the simulation of atmospheric ows over complex terrain, using OpenFOAM. For this aim, tools and procedures were developed apart from this code for the preprocessing and data extraction, which were thereafter applied in the simulation of a real case. For the generation of the computational domain, a systematic method able to translate the terrain elevation model to a native OpenFOAM format (blockMeshDict) was developed. The outcome was a structured mesh, in which the user has the ability to de ne the number of control volumes and its dimensions. With this procedure, the di culties of case set up and the high computation computational e ort reported in literature associated to the use of snappyHexMesh, the OpenFOAM resource explored until then for the accomplishment of this task, were considered to be overwhelmed. Developed procedures for the generation of boundary conditions allowed for the automatic creation of idealized inlet vertical pro les, de nition of wall functions boundary conditions and the calculation of internal eld rst guesses for the iterative solution process, having as input experimental data supplied by the user. The applicability of the generated boundary conditions was limited to the simulation of turbulent, steady-state, incompressible and neutrally strati ed atmospheric ows, always recurring to RaNS (Reynolds-averaged Navier-Stokes) models. For the modelling of terrain roughness, the developed procedure allowed to the user the de nition of idealized conditions, like an uniform aerodynamic roughness length or making its value variable as a function of topography characteristic values, or the using of real site data, and it was complemented by the development of techniques for the visual inspection of generated roughness maps. The absence and the non inclusion of a forest canopy model limited the applicability of this procedure to low aerodynamic roughness lengths. The developed tools and procedures were then applied in the simulation of a neutrally strati ed atmospheric ow over the Askervein hill. In the performed simulations was evaluated the solution sensibility to di erent convection schemes, mesh dimensions, ground roughness and formulations of the k - ε and k - ω models. When compared to experimental data, calculated values showed a good agreement of speed-up in hill top and lee side, with a relative error of less than 10% at a height of 10 m above ground level. Turbulent kinetic energy was considered to be well simulated in the hill windward and hill top, and grossly predicted in the lee side, where a zone of ow separation was also identi ed. Despite the need of more work to evaluate the importance of the downstream recirculation zone in the quality of gathered results, the agreement between the calculated and experimental values and the OpenFOAM sensibility to the tested parameters were considered to be generally in line with the simulations presented in the reviewed bibliographic sources.

Modelling the Contribution of 40K, 232Th and 226Ra to Radiation Dose and Risk from Airborne Discharges of Coal-Fired Power Plants

Coal contains trace elements and naturally occurring radionuclides such as 40K, 232Th, 238U. When coal is burned, minerals, including most of the radionuclides, do not burn and concentrate in the ash several times in comparison with their content in coal. Usually, a small fraction of the fly ash produced (2-5%) is released into the atmosphere. The activities released depend on many factors (concentration in coal, ash content and inorganic matter of the coal, combustion temperature, ratio between bottom and fly ash, filtering system). Therefore, marked differences should be expected between the by-products produced and the amount of activity discharged (per unit of energy produced) from different coal-fired power plants. In fact, the effects of these releases on the environment due to ground deposition have been received some attention but the results from these studies are not unanimous and cannot be understood as a generic conclusion for all coal-fired power plants. In this study, the dispersion modelling of natural radionuclides was carried out to assess the impact of continuous atmospheric releases from a selected coal plant. The natural radioactivity of the coal and the fly ash were measured and the dispersion was modelled by a Gaussian plume estimating the activity concentration at different heights up to a distance of 20 km in several wind directions. External and internal doses (inhalation and ingestion) and the resulting risk were calculated for the population living within 20 km from the coal plant. In average, the effective dose is lower than the ICRP’s limit and the risk is lower than the U.S. EPA’s limit. Therefore, in this situation, the considered exposure does not pose any risk. However, when considering the dispersion in the prevailing wind direction, these values are significant due to an increase of 232Th and 226Ra concentrations in 75% and 44%, respectively.

Multi-agent simulation of continental, regional, and micro electricity markets

Renewable based power generation has significantly increased over the last years. However, this process has evolved separately from electricity markets, leading to an inadequacy of the present market models to cope with huge quantities of renewable energy resources, and to take full advantage of the presently existing and the increasing envisaged renewable based and distributed energy resources. This paper proposes the modelling of electricity markets at several levels (continental, regional and micro), taking into account the specific characteristics of the players and resources involved in each level and ensuring that the proposed models accommodate adequate business models able to support the contribution of all the resources in the system, from the largest to the smaller ones. The proposed market models are integrated in MASCEM (Multi- Agent Simulator of Competitive Electricity Markets), using the multi agent approach advantages for overcoming the current inadequacy and significant limitations of the presently existing electricity market simulators to deal with the complex electricity market models that must be adopted.

Fractional dynamics in DNA

This paper addresses the DNA code analysis in the perspective of dynamics and fractional calculus. Several mathematical tools are selected to establish a quantitative method without distorting the alphabet represented by the sequence of DNA bases. The association of Gray code, Fourier transform and fractional calculus leads to a categorical representation of species and chromosomes.