Abstract: We generalize the Gielis Superformula by extending the R. Chacon approach, but avoiding the use of Jacobi elliptic functions. The obtained results are extended to the three-dimensional case. Several new shapes are derived by using the computer algebra system Mathematica(C).

Abstract: Gielis curves and surfaces can describe a wide range of natural shapes and they have been used in various studies in biology and physics as descriptive tool. This has stimulated the generalization of widely used computational methods. Here we show that proper normalization of the Levenberg-Marquardt algorithm allows for efficient and robust reconstruction of Gielis curves, including self-intersecting and asymmetric curves, without increasing the overall complexity of the algorithm. Then, we show how complex curves of k-type can be constructed and how solutions to the Dirichlet problem for the Laplace equation on these complex domains can be derived using a semi-Fourier method. In all three methods, descriptive and computational power and efficiency is obtained in a surprisingly simple way.

Abstract: Gielis transformations, with their origin in botany, are used to define square waves and trigonometric functions of higher order. They are rewritten in terms of Chebyshev polynomials. The origin of both, a uniform descriptor and the origin of orthogonal polynomials, can be traced back to a letter of Guido Grandi to Leibniz in 1713 on the mathematical description of the shape of flowers. In this way geometrical description and analytical tools are seamlessly combined.

Abstract: Fibonacci numbers are a very popular subject in mathematics, culture and science. A major open question is why the ancient Greeks overlooked this series, while they were very familiar with the golden mean and division in extreme and mean ratio. Furthermore, they could compute the square root of five to a high degree of precision using Theon 's ladder. This fact is based on tables built with side and diagonal numbers, and it is a simple and incredibly efficient method to compute roots of integers, though it is little known even now among most of the experts. The biologist D 'Arcy Wentworth Thompson showed that the same method could be used to generate the Fibonacci series using a simple shift in the computation of the tables. He argues, quite convincingly, that the ancient Greeks could not have overlooked this. Actually, the same method can be used to generate all possible regular phyllotaxis patterns.

Abstract: Our scientific and technological worldviews are largely dominated by the concepts of entropy and complexity. Originating in 19th-century thermodynamics, the concept of entropy merged with information in the last century, leading to definitions of entropy and complexity by Kolmogorov, Shannon and others. In its simplest form, this worldview is an application of the normal rules of arithmetic. In this worldview, when tossing a coin, a million heads or tails in a row is theoretically possible, but impossible in practice and in real life. On this basis, the impossible (in the binary case, the outermost entries of Pascal's triangle xn and yn for large values of n) can be safely neglected, and one can concentrate fully on what is common and what conforms to the law of large numbers, in fields ranging from physics to sociology and everything in between. However, in recent decades it has been shown that what is most improbable tends to be the rule in nature. Indeed, if one combines the outermost entries xn and yn with the normal rules of arithmetic, either addition or multiplication, one obtains Lamé curves and power laws respectively. In this article, some of these correspondences are highlighted, leading to a double conclusion. First, Gabriel Lamé's geometric footprint in mathematics and the sciences is enormous. Second, conic sections are at the core once more. Whereas mathematics so far has been exclusively the language of patterns in the sciences, the door is opened for mathematics to also become the language of the individual. The probabilistic worldview and Lamé's footprint can be seen as dual methods. In this context, it is to be expected that the notions of information, complexity, simplicity and redundancy benefit from this different viewpoint.

Abstract: In een context van stijgende waterschaarste verkennen wij, naar ons weten voor het eerst in Vlaanderen, publieke steun voor de behandeling en het hergebruik van afvalwater als drinkwater. Vlaanderen is vandaag een van de weinige regio’s waar afvalwater reeds gerecycleerd wordt voor drinkwaterdoeleinden. Dit gebeurt op kleinschalig niveau en de uitbreiding hiervan is vandaag een van de Vlaamse beleidsdoelstellingen. Internationale voorbeelden toonden echter dat een gebrek aan publieke steun een aanzienlijk obstakel kan zijn. Vaak worden gezondheids- en veiligheidsbezorgdheden aangehaald als oorzaak voor het beperkte draagvlak. Minder is geweten over de socio-demografische distributie van dit draagvlak. Daarbovenop blijft er onduidelijkheid over de samenhang tussen socio-demografische kenmerken en gezondheids- en veiligheidsbezorgdheden. Met behulp van een enquête uitgevoerd in Vlaanderen (N=2309), bestudeerden wij ten eerste deze socio-demografische verschillen op basis van bivariate associaties (gender, opleidingsniveau, leeftijd en woonplaats). Ten tweede construeerden we een padmodel om te onderzoeken of deze verschillen verklaard kunnen worden aan de hand van gezondheids- en veiligheidsbezorgdheden. Onze resultaten toonden dat publieke steun voor afvalwaterhergebruik voor drinkwaterdoeleinden in Vlaanderen beperkt is. Het draagvlak was het laagst bij oudere mensen, vrouwen, lager geschoolde groepen en mensen die niet in de Provincie Antwerpen wonen. Voor een groot deel konden socio-demografische verschillen verklaard worden door hogere gezondheids- en veiligheidsbezorgdheden bij vrouwen, lager geschoolden en mensen uit West- en Oost-Vlaanderen. Dit suggereert een gebrek aan vertrouwen in waterexperts en -technologie bij bepaalde socio-demografische groepen, wat zich vertaalt in een verminderde publieke steun voor afvalwaterhergebruik. Op basis van deze bevindingen bespreken we een aantal potentiële actiestrategieën om publieke oppositie te anticiperen en proactief publieke steun te verwerven via doelgerichte (risico)communicatie.

Abstract: Reuse of growth medium after biomass harvesting is a cost-saving approach to improve the economic feasibility of algae mass cultivation. Algal exudates, cell debris and varying amounts of residual nutrients, impose challenges to the recycling of spent medium. In this study, the potential of combining reused medium from different algae species for growing monocultures of other algal strains was evaluated by making use of three successive cultivation setups with increasing volume; 400 mL in turbidostat mode, 2.6 L and 220 L in semi-continuous mode. Cultivation on replenished medium derived from Nannochloropsis sp. and Tisochrysis lutea, had no adverse effect on the productivity of either of the strains, regardless of whether they were grown in their own recycled medium or that of the other alga. Microfiltration of the reused medium proved to be sufficient to avoid cross-contamination. Moreover, a substantial average reduction in water footprint (77%) and nutrient cost (68% or 9 (sic).kg(-1) dry biomass) was achieved. Extension and validation of the medium recycling approach to other economically interesting algae species can contribute to improving the economic feasibility of large scale microalgae production systems.

Abstract: The definition of Gielis curves allows for the representation of self intersecting curves. The analysis and the understanding of these representations is of major interest for the analytical representation of sectors bounded by multiple subsets of curves (or surfaces), as this occurs for instance in many natural objects. We present a construction scheme based on R-functions to build signed potential fields with guaranteed differential properties, such that their zero-set corresponds to the outer, the inner envelop, or combined subparts of the curve. Our framework is designed to allow for the definition of composed domains built upon Boolean operations between several distinct objects or some subpart of self-intersecting curves, but also provides a representation for soft blending techniques in which the traditional Boolean union and intersection become special cases of linear combinations between the objects' potential fields. Finally, by establishing a connection between R-functions and Lame curves, we can extend the domain of the p parameter within the R-p-function from the set of the even positive numbers to the real numbers strictly greater than 1, i.e. p is an element of]1, +infinity[.

Abstract: The membrane life-time has a strong impact on competitivity and viability of MBRs. This study critically analyzes the membrane life-time concept, approaching it through different assessment methods. A full scale MBR's membrane life-time was assessed on the following: (i) maintaining the permeate flow throughput to the MBR; (ii) the permeability decline; (iii) oxidative aging; (iv) the increase in energy costs; and (v) mechanical aging. The method based on permeability decline provides a membrane life-time estimate up to a theoretical end. It was further elaborated inherently to operations with no long-term flux decline. The increase in operating pressure remains the main end-of-life trigger for deciding when to replace membrane modules. On the contrary, mechanical and permeate flow throughput analysis of the data are not able to provide a clear estimate of the membrane life-time. As for the membrane life-time estimation based on chlorine contact, it was found to be too optimistic. Complete irreversible fouling occurs before maximum contact time with chlorine is reached. At end-of-life operating conditions, the energy consumption raised of 170% due to the reduced flow rate. The cost raise appears high but still affordable. Earlier membrane replacement thus can never be counterbalanced by energy costs saving. (C) 2012 Elsevier B.V. All rights reserved.