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“Plant morphology and function, geometric morphometrics, and modelling : decoding the mathematical secrets of plants”. Gao J, Huang W, Gielis J, Shi P page 224 p. (2023).
Abstract: Delve into the diverse aspects of plant morphology, their responses to global climate change, and the spatiotemporal dynamics of forest productivity. Join us on a journey through the intricate web of plant characteristics and their impact on the environment.
Keywords: ME3 Book as editor; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.3390/BOOKS978-3-0365-9423-1
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“Drinking waste? An exploration of public support for wastewater reuse in Flanders”. Geerts R, Vandermoere F, Halet D, Joos P, Van Den Steen K, Van Meenen E, Blust R, Van Winckel T, Vlaeminck S, (2020)
Keywords: P3 Proceeding; Sociology; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL); Centre for Research on Environmental and Social Change
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“Ik drink (geen) afval! Een exploratieve studie naar socio-demografische verschillen in publieke steun voor het hergebruik van afvalwater in Vlaanderen”. Geerts R, Vandermoere F, Halet D, Van Winckel T, Joos P, Van Den Steen K, Van Meenen E, Blust R, Vlaeminck SE, Vlaams tijdschrift voor overheidsmanagement , 51 (2020)
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.
Keywords: A1 Journal article; Sociology; Sustainable Energy, Air and Water Technology (DuEL); Centre for Research on Environmental and Social Change
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“Bottle or tap? Toward an integrated approach to water type consumption”. Geerts R, Vandermoere F, Van Winckel T, Halet D, Joos P, Van Den Steen K, Van Meenen E, Blust R, Borregán-Ochando E, Vlaeminck SE, Water Research 173, 115578 (2020). http://doi.org/10.1016/J.WATRES.2020.115578
Abstract: While in many countries, people have access to cheap and safe potable tap water, the global consumption of bottled water is rising. Flanders, Belgium, where this study is located, has an exceptionally high consumption of bottled water per capita. However, in the interest of resource efficiency and global environmental challenges, the consumption of tap water is preferable. To our knowledge, an integrated analysis of the main reasons why people consume tap and bottled water is absent in Flanders, Belgium. Using Flemish survey data (N = 2309), we first compared tap and bottled water consumers through bivariate correlation analysis. Subsequently, path modelling techniques were used to further investigate these correlations. Our results show that bottled water consumption in Flanders is widespread despite environmental and financial considerations. For a large part, this is caused by negative perceptions about tap water. Many consumers consider it unhealthy, unsafe and prefer the taste of bottled water. Furthermore, we found that the broader social context often inhibits the consumption of tap water. On the one hand, improper infrastructures (e.g. lead piping) can limit access to potable tap water. On the other hand, social norms exist that promote bottled water. Lastly, results suggest that the consumption of bottled water is most common among men, older people and less educated groups. We conclude that future research and policy measures will benefit from an approach that integrates all behavioural aspects associated with water type consumption. This will enable both governments and tap water companies to devise more effective policies to manage and support tap water supply networks.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL); Centre for Research on Environmental and Social Change
Impact Factor: 12.8
Times cited: 2
DOI: 10.1016/J.WATRES.2020.115578
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Gielis J (2021) Double helix of phyllotaxis : analysis of the geometric model of plant morphogenesis, by Boris Rozin. 139–140
Keywords: Review; Sustainable Energy, Air and Water Technology (DuEL)
Impact Factor: 4.25
DOI: 10.1086/714470
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“Er bestaan geen absurde, irrationele, onregelmatige of onderling niet-onmeetbare meetkundige getallen”. Gielis J, Wiskunde en onderwijs 47, 23 (2021)
Keywords: A2 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
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Gielis J (2017) The geometrical beauty of plants. 229 p
Keywords: MA3 Book as author; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.2991/978-94-6239-151-2
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“Phi-bonacci in Ancient Greece”. Gielis J, Symmetry : culture and science 32, 25 (2021). http://doi.org/10.26830/SYMMETRY_2021_1_025
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.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.26830/SYMMETRY_2021_1_025
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“Temperate bamboos in ornamental horticulture: differentiators and spillover effects into the 21st century”. Gielis J page 603 (2012).
Keywords: H3 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
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Gielis J (2023) Fred Van Oystaeyen : Time hybrids: a new generic theory of reality. 347–351
Keywords: Review; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.26830/SYMMETRY_2023_3_357
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“Simon Stevin as a central figure in the development of abstract algebra and generic programming”. Gielis J, Symmetry : culture and science 34, 155 (2023). http://doi.org/10.26830/SYMMETRY_2023_2_155
Abstract: Simon Stevin (1548-1620) is mainly known for the decimal system and his Clootkrans proof. His influence is also profound in infinitesimal calculus, mechanics, and even in abstract algebra and today’s conception of polynomials, algorithms, and generic programming. Here we review his influence as assessed in generic programming. According to Dr. Stepanov, one of the most influential researchers in generic programming, Stevin’s work on polynomials can be regarded as the essence of generic programming: an algorithm from one domain can be applied in another similar domain.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.26830/SYMMETRY_2023_2_155
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“Conquering Mount Improbable”. Gielis J, , 153 (2023). http://doi.org/10.55060/s.atmps.231115.013
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.
Keywords: P1 Proceeding; Economics; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.55060/s.atmps.231115.013
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“The apeirogon and dual numbers”. Gielis J, Brasili S, Symmetry : culture and science 32, 157 (2021). http://doi.org/10.26830/SYMMETRY_2021_2_157
Abstract: The richness, diversity, connection, depth and pleasure of studying symmetry continue to open doors. Here we report a connection between Coxeter's Apeirogon and the geometry associated with pictorial space, parabolic rotation and dual numbers.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.26830/SYMMETRY_2021_2_157
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“Proceedings of the 1st International Symposium on Square Bamboos and the Geometree (ISSBG 2022)”. Gielis J, Brasili S page xi, 175 p. (2023).
Keywords: ME3 Book as editor; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.55060/s.atmps.231115.000
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“The common descent of biological shape description and special functions”. Gielis J, Caratelli D, de Jong van Coevorden M, Ricci PE page 119 (2018).
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.
Keywords: H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1007/978-3-319-75647-9_10
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“A biogeometrical model for corolla fusion in Asclepiad flowers”. Gielis J, Caratelli D, Fougerolle Y, Ricci PE, Gerats T page 83 (2017).
Abstract: The molecular genetics of flower development have been studied extensively for more than two decades. Fusion of organs and the tendency to oligomery, important characteristics of flower evolution, so far have remained fairly elusive. We present a geometric model for shape and fusion in the corolla of Asclepiads. Examples demonstrate how fusion of petals creates stable centers, a prerequisite for the formation of complex pollination structures via congenital and postgenital fusion events, with the formation of de novo organs, specific to Asclepiads. The development of the corolla reduces to simple inequalities from the MATHS-BOX. The formation of stable centers and of bell and tubular shapes in flowers are immediate and logical consequences of the shape. Our model shows that any study on flowers, especially in evo-devo perspective should be performed within the wider framework of polymery and oligomery and of fusion and synorganization.
Keywords: H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.2991/978-94-6239-261-8_7
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“Universal natural shapes : from unifying shape description to simple methods for shape analysis and boundary value problems”. Gielis J, Caratelli D, Fougerolle Y, Ricci PE, Tavkelidze I, Gerats T, PLoS ONE 7, e29324 (2012). http://doi.org/10.1371/JOURNAL.PONE.0029324
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.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1371/JOURNAL.PONE.0029324
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“A note on spirals and curvature”. Gielis J, Caratelli D, Shi P, Ricci PE, Growth and form 1, 1 (2020). http://doi.org/10.2991/GAF.K.200124.001
Abstract: Starting from logarithmic, sinusoidal and power spirals, it is shown how these spirals are connected directly with Chebyshev polynomials, Lamé curves, with allometry and Antonelli-metrics in Finsler geometry. Curvature is a crucial concept in geometry both for closed curves and equiangular spirals, and allowed Dillen to give a general definition of spirals. Many natural shapes can be described as a combination of one of two basic shapes in nature—circle and spiral—with Gielis transformations. Using this idea, shape description itself is used to develop a novel approach to anisotropic curvature in nature. Various examples are discussed, including fusion in flowers and its connection to the recently described pseudo-Chebyshev functions.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.2991/GAF.K.200124.001
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“Bulky knots and links generated by cutting generalized Mobius-Listing bodies and applications in the natural sciences”. Gielis J, Caratelli D, Tavkelidze I, Fougerolle Y, Ricci PE, Gerats T page 167 (2013).
Keywords: H2 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
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“The general case of cutting GML bodies : the geometrical solution”. Gielis J, Caratelli D, Tavkhelidze I page 397 (2020).
Keywords: H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1007/978-3-030-56323-3_31
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“Towards a geometrical theory of morphology and morphogenesis”. Gielis J, Ding Y, Shi P, (2016)
Keywords: P3 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
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“Lamé, curves and Rvachev's R-functions”. Gielis J, Grigolia R, Sn –, 1512-0066 37, 1 (2022)
Abstract: Gielis transformations are a generalization of Lame curves. To combine domains, we can make use of the natural alliance between Lame's work and Rvachev's R-functions. A logical next step is the extension to n-valued logic dening dierent partitions.
Keywords: A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
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“A note about generalized forms of the Gielis formula”. Gielis J, Natalini P, Ricci PE page 107 (2017).
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).
Keywords: H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.2991/978-94-6239-261-8_8
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“Proceedings of the 9th World Bamboo Congress, Antwerp 2012”. Gielis J, Potters G, (2012)
Keywords: P3 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
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“The Möbius phenomenon in Generalized Möbius-Listing surfaces and bodies, and Arnold's Cat phenomenon”. Gielis J, Ricci PE, Tavkhelidze I, Advanced Studies : Euro-Tbilisi Mathematical Journal 14, 17 (2021). http://doi.org/10.3251/ASETMJ/1932200812
Abstract: Möbius bands have been studied extensively, mainly in topology. Generalized Möbius-Listing surfaces and bodies providing a full geometrical generalization, is a quite new field, motivated originally by solutions of boundary value problems. Analogous to cutting of the original Möbius band, for this class of surfaces and bodies, results have been obtained when cutting such bodies or surfaces. In general, cutting leads to interlinked and intertwined different surfaces or bodies, resulting in very complex systems. However, under certain conditions, the result of cutting can be a single surface or body, which reduces complexity considerably. Our research is motivated by this reduction of complexity. In the study of cutting Generalized Möbius-Listing bodies with polygons as cross section, the conditions under which a single body results, displaying the Möbius phenomenon of a one-sided body, have been determined for even and odd polygons. These conditions are based on congruence and rotational symmetry of the resulting cross sections after cutting, and on the knife cutting the origin. The Möbius phenomenon is important, since the process of cutting (or separation of zones in a GML body in general) then results in a single body, not in different, intertwined domains. In all previous works it was assumed that the cross section of the GML bodies is constant, but the main result of this paper is that it is sufficient that only one cross section on the whole GML structure meets the conditions for the Möbius phenomenon to occur. Several examples are given to illustrate this.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.3251/ASETMJ/1932200812
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“Modeling in mathematics : proceedings of the second Tbilisi-Salerno workshop on modeling in mathematics”. Gielis J, Ricci PE, Tavkhelidze I page 185 p. (2017).
Keywords: ME3 Book as editor; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.2991/978-94-6239-261-8
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“Lamé-Gielis curves in biology and geometry”. Gielis J, Shi P, Beirinckx B, Caratelli D, Ricci PE, (2021)
Keywords: P3 Proceeding; Sustainable Energy, Air and Water Technology (DuEL)
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“Universal equations : a fresh perspective”. Gielis J, Shi P, Caratelli D, Growth and Form (2022)
Abstract: A uniform description of natural shapes and phenomena is an important goal in science. Such description should check some basic principles, related to 1) the complexity of the model, 2) how well its fits real objects, phenomena and data, and 3) ia direct connection with optimization principles and the calculus of variations. In this article, we present nine principles, three for each group, and we compare some models with a claim to universality. It is also shown that Gielis Transformations and power laws have a common origin in conic sections
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
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“About “bulky” links, generated by generalized Möbius-Listing bodies”. Gielis J, Tavkelidze I, Ricci PE page 115 (2011).
Keywords: H3 Book chapter; Sustainable Energy, Air and Water Technology (DuEL)
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“The general case of cutting of Generalized Möbius-Listing surfaces and bodies”. Gielis J, Tavkhelidze I, 4Open 3, 7 (2020). http://doi.org/10.1051/FOPEN/2020007
Abstract: The original motivation to study Generalized Möbius-Listing GML surfaces and bodies was the observation that the solution of boundary value problems greatly depends on the domains. Since around 2010 GML’s were merged with (continuous) Gielis Transformations, which provide a unifying description of geometrical shapes, as a generalization of the Pythagorean Theorem. The resulting geometrical objects can be used for modeling a wide range of natural shapes and phenomena. The cutting of GML bodies and surfaces, with the Möbius strip as one special case, is related to the field of knots and links, and classifications were obtained for GML with cross sectional symmetry of 2, 3, 4, 5 and 6. The general case of cutting GML bodies and surfaces, in particular the number of ways of cutting, could be solved by reducing the 3D problem to planar geometry. This also unveiled a range of connections with topology, combinatorics, elasticity theory and theoretical physics.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1051/FOPEN/2020007
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