MATHEMATICAL MODELS AND POLYHEDRAL STUDIES FOR INTEGRAL SHEET METAL DESIGN

We deal with the optimization of the production of branched sheet metal products. New forming techniques for sheet metal give rise to a wide variety of possible profiles and possible ways of production. In particular, we show how the problem of producing a given profile geometry can be modeled as a discrete optimization problem. We provide a theoretical analysis of the model in order to improve its solution time. In this context we give the complete convex hull description of some substructures of the underlying polyhedron. Moreover, we introduce a new class of facet-defining inequalities that represent connectivity constraints for the profile and show how these inequalities can be separated in polynomial time. Finally, we present numerical results for various test instances, both real-world and academic examples.

Metal biosorption onto dry biomass of Arthrospira (Spirulina) platensis and Chlorella vulgaris: Multi-metal systems

Binary and ternary systems of Ni2+, Zn2+, and Pb2+ were investigated at initial metal concentrations of 0.5, 1.0 and 2.0 mM as competitive adsorbates using Arthrospira platensis and Chlorella vulgaris as biosorbents. The experimental results were evaluated in terms of equilibrium sorption capacity and metal removal efficiency and fitted to the multi-component Langmuir and Freundlich isotherms. The pseudo second order model of Ho and McKay described well the adsorption kinetics, and the FT-IR spectroscopy confirmed metal binding to both biomasses. Ni2+ and Zn2+ interference on Pb2+ sorption was lower than the contrary, likely due to biosorbent preference to Pb. In general, the higher the total initial metal concentration, the lower the adsorption capacity. The results of this study demonstrated that dry biomass of C. vulgaris behaved as better biosorbent than A. platensis and suggest its use as an effective alternative sorbent for metal removal from wastewater. (C) 2012 Elsevier B.V. All rights reserved.