The nonexistence of spurious solutions to discrete, two-point boundary value problems

We investigate difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations. We formulate conditions under which all solutions to the discrete problem satisfy certain a priori bounds which axe independent of the step-size. As a result, the nonexistence of spurious solutions are guaranteed. Some existence and convergence theorems for solutions to the discrete problem are also presented. (C) 2002 Elsevier Science Ltd. All rights reserved.

Difference equations in Banach spaces

Difference equations which discretely approximate boundary value problems for second-order ordinary differential equations are analysed. It is well known that the existence of solutions to the continuous problem does not necessarily imply existence of solutions to the discrete problem and, even if solutions to the discrete problem are guaranteed, they may be unrelated and inapplicable to the continuous problem. Analogues to theorems for the continuous problem regarding a priori bounds and existence of solutions are formulated for the discrete problem. Solutions to the discrete problem are shown to converge to solutions of the continuous problem in an aggregate sense. An example which arises in the study of the finite deflections of an elastic string under a transverse load is investigated. The earlier results are applied to show the existence of a solution; the sufficient estimates on the step size are presented. (C) 2003 Elsevier Science Ltd. All rights reserved.

The Galilean turn in population ecology

The standard mathematical models in population ecology assume that a population's growth rate is a function of its environment. In this paper we investigate an alternative proposal according to which the rate of change of the growth rate is a function of the environment and of environmental change. We focus on the philosophical issues involved in such a fundamental shift in theoretical assumptions, as well as on the explanations the two theories offer for some of the key data such as cyclic populations. We also discuss the relationship between this move in population ecology and a similar move from first-order to second-order differential equations championed by Galileo and Newton in celestial mechanics.

The uniqueness of solutions to discrete, victor, two-point boundary value problems

Difference equations which may arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations are investigated and conditions are formulated under which solutions to the discrete problem are unique. Some existence, uniqueness implies existence, and convergence theorems for solutions to the discrete problem are also presented.

Theoretical and experimental studies of unbraced tubular trusses allowing for torsional stiffness

This paper describes the buckling phenomenon of a tubular truss with unsupported length through a full-scale test and presents a practical computational method for the design of the trusses allowing for the contribution of torsional stiffness against buckling, of which the effect has never been considered previously by others. The current practice for the design of a planar truss has largely been based on the linear elastic approach which cannot allow for the contribution of torsional stiffness and tension members in a structural system against buckling. The over-simplified analytical technique is unable to provide a realistic and an economical design to a structure. In this paper the stability theory is applied to the second-order analysis and design of the structural form, with detailed allowance for the instability and second-order effects in compliance with design code requirements. Finally, the paper demonstrates the application of the proposed method to the stability design of a commonly adopted truss system used in support of glass panels in which lateral bracing members are highly undesirable for economical and aesthetic reasons.

On the evaluation of some differential formulations for the pom-pom constitutive model

In recent years, progress has been made in modelling long chain branched polymers by the introduction of the so-called pompom model. Initially developed by McLeish and Larson (1998), the model has undergone several improvements or alterations, leading to the development of new formulations. Some of these formulations however suffer from certain mathematical defects. The purpose of the present paper is to review some of the formulations of the pom-pom constitutive model, and to investigate their possible mathematical defects. Next, an alternative formulation is proposed, which does not appear to exhibit mathematical defects, and we explore its modelling performance by comparing the predictions with experiments in non-trivial rheometric flows of an LDPE melt. The selected rheometric flows are the double step strain, as well as the large amplitude oscillatory shear experiments. For LAOS experiments, the comparison involves the use of Fourier-transform analysis.

Remoção de metais usando casca de amendoim

Mestrado em Engenharia Química

Seismic imaging of the western Iberian crust using ambient noise: Boundaries and internal structure of the Iberian Massif

We present new Rayleigh-wave dispersion maps of the western Iberian Peninsula for periods between 8 and 30 s, obtained from correlations of seismic ambient noise, following the recent increase in seismic broadband network density in Portugal and Spain. Group velocities have been computed for each station pair using the empirical Green's functions generated by cross-correlating one-day-length seismic ambient-noise records. The resulting high-path density allows us to obtain lateral variations of the group velocities as a function of period in cells of 0.5 degrees x 0.5 degrees with an unprecedented resolution. As a result we were able to address some of the unknowns regarding the lithospheric structure beneath SW Iberia. The dispersion maps allow the imaging of the major structural units, namely the Iberian Massif, and the Lusitanian and Algarve Meso-Cenozoic basins. The Cadiz Gulf/Gibraltar Strait area corresponds to a strong low-velocity anomaly, which can be followed to the largest period inverted, although slightly shifted to the east at longer periods. Within the Iberian Massif, second-order perturbations in the group velocities are consistent with the transitions between tectonic units composing the massif. (C) 2013 Elsevier B.V. All rights reserved.

Basic dyestuffs removal from textile effluents using feathers: equilibrium, kinetic and column studies

This research work has been focused in the study of gallinaceous feathers, a waste that may be valorised as sorbent, to remove the Dark Blue Astrazon 2RN (DBA) from Dystar. This study was focused on the following aspects: optimization of experimental conditions through factorial design methodology, kinetic studies into a continuous stirred tank adsorber (at pH 7 and 20ºC), equilibrium isotherms (at pH 5, 7 and 9 at 20 and 45ºC) and column studies (at 20ºC, at pH 5, 7 and 9). In order to evaluate the influence of the presence of other components in the sorption of the dyestuff, all experiments were performed both for the dyestuff in aqueous solution and in real textile effluent. The pseudo-first and pseudo-second order kinetic models were fitted to the experimental data, being the latter the best fit for the aqueous solution of dyestuff. For the real effluent both models fit the experimental results and there is no statistical difference between them. The Central Composite Design (CCD) was used to evaluate the effects of temperature (15 - 45ºC) and pH (5 - 9) over the sorption in aqueous solution. The influence of pH was more significant than temperature. The optimal conditions selected were 45ºC and pH 9. Both Langmuir and Freundlich models could fit the equilibrium data. In the concentration range studied, the highest sorbent capacity was obtained for the optimal conditions in aqueous solution, which corresponds to a maximum capacity of 47± 4 mg g-1. The Yoon-Nelson, Thomas and Yan’s models fitted well the column experimental data. The highest breakthrough time for 50% removal, 170 min, was obtained at pH 9 in aqueous solution. The presence of the dyeing agents in the real wastewater decreased the sorption of the dyestuff mostly for pH 9, which is the optimal pH. The effect of pH is less pronounced in the real effluent than in aqueous solution. This work shows that feathers can be used as sorbent in the treatment of textile wastewaters containing DBA.

On cluster analysis of complex and heterogeneous data

3rd SMTDA Conference Proceedings, 11-14 June 2014, Lisbon Portugal.

Nonlinear mixture model for hyperspectral unmixing

Proceedings of International Conference - SPIE 7477, Image and Signal Processing for Remote Sensing XV - 28 September 2009

Demixing instability in coil-rod blends undergoing polycondensation reactions

The authors extend their earlier work on the stability of a reacting binary polymer blend with respect to demixing [D. J. Read, Macromolecules 31, 899 (1998); P. I. C. Teixeira , Macromolecules 33, 387 (2000)] to the case where one of the polymers is rod-like and may order nematically. As before, the authors combine the random phase approximation for the free energy with a Markov chain model for the chemistry to obtain the spinodal as a function of the relevant degrees of reaction. These are then calculated by assuming a simple second-order chemical kinetics. Results are presented, for linear systems, which illustrate the effects of varying the proportion of coils and rods, their relative sizes, and the strength of the nematic interaction between the rods. (c) 2007 American Institute of Physics.

Copper, nickel and zinc removal by peanut hulls: batch and column studies in mono, tri-component systems and with real effluent

The main goal of this research study was the removal of Cu(II), Ni(II) and Zn(II) from aqueous solutions using peanut hulls. This work was mainly focused on the following aspects: chemical characterization of the biosorbent, kinetic studies, study of the pH influence in mono-component systems, equilibrium isotherms and column studies, both in mono and tri-component systems, and with a real industrial effluent from the electroplating industry. The chemical characterization of peanut hulls showed a high cellulose (44.8%) and lignin (36.1%) content, which favours biosorption of metal cations. The kinetic studies performed indicate that most of the sorption occurs in the first 30 min for all systems. In general, a pseudo-second order kinetics was followed, both in mono and tri-component systems. The equilibrium isotherms were better described by Freundlich model in all systems. Peanut hulls showed higher affinity for copper than for nickel and zinc when they are both present. The pH value between 5 and 6 was the most favourable for all systems. The sorbent capacity in column was 0.028 and 0.025 mmol g-1 for copper, respectively in mono and tri-component systems. A decrease of capacity for copper (50%) was observed when dealing with the real effluent. The Yoon-Nelson, Thomas and Yan’s models were fitted to the experimental data, being the latter the best fit.

Removal of Cd(II), Zn(II) and Pb(II) from aqueous solutions by brown marine macro algae: kinetic modelling

Specific marine macro algae species abundant at the Portuguese coast (Laminaria hyperborea, Bifurcaria bifurcata, Sargassum muticum and Fucus spiralis) were shown to be effective for removing toxic metals (Cd(II), Zn(II) and Pb(II)) from aqueous solutions. The initial metal concentrations in solution were about 75–100 mg L−1. The observed biosorption capacities for cadmium, zinc and lead ions were in the ranges of 23.9–39.5, 18.6–32.0 and 32.3–50.4 mg g−1, respectively. Kinetic studies revealed that the metal uptake rate was rather fast, with 75% of the total amount occurring in the first 10 min for all algal species. Experimental data were well fitted by a pseudo-second order rate equation. The contribution of internal diffusion mechanism was significant only to the initial biosorption stage. Results indicate that all the studied macro algae species can provide an efficient and cost-effective technology for eliminating heavy metals from industrial effluents.

Copper and lead removal by peanut hulls: equilibrium and kinetic studies

This research work aims to study the use of peanut hulls, an agricultural and food industry waste, for copper and lead removal through equilibrium and kinetic parameters evaluation. Equilibrium batch studies were performed in a batch adsorber. The influence of initial pH was evaluated (3–5) and it was selected between 4.0 and 4.5. The maximum sorption capacities obtained for the Langmuir model were 0.21 ± 0.03 and 0.18 ± 0.02 mmol/g, respectively for copper and lead. In bi-component systems, competitive sorption of copper and lead was verified, the total amount adsorbed being around 0.21 mmol of metal per gram of material in both mono and bi-component systems. In the kinetic studies equilibrium was reached after 200 min contact time using a 400 rpm stirring rate, achieving 78% and 58% removal, in mono-component system, for copper and lead respectively. Their removal follows a pseudo-second-order kinetics. These studies show that most of the metals removal occurred in the first 20 min of contact, which shows a good uptake rate in all systems.