“De kleine boerderij : twee bijzondere tuinkamers”. Vermander C, De Wael J, Gielis J, Groencontact 45, 14 (2019)
Keywords: A2 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
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“A general leaf area geometric formula exists for plants evidence from the simplified Gielis equation”. Shi P, Ratkowsky DA, Li Y, Zhang L, Lin S, Gielis J, Forests (19994907) 9, 714 (2018). http://doi.org/10.3390/F9110714
Abstract: Plant leaves exhibit diverse shapes that enable them to utilize a light resource maximally. If there were a general parametric model that could be used to calculate leaf area for different leaf shapes, it would help to elucidate the adaptive evolutional link among plants with the same or similar leaf shapes. We propose a simplified version of the original Gielis equation (SGE), which was developed to describe a variety of object shapes ranging from a droplet to an arbitrary polygon. We used this equation to fit the leaf profiles of 53 species (among which, 48 bamboo plants, 5 woody plants, and 10 geographical populations of a woody plant), totaling 3310 leaves. A third parameter (namely, the floating ratio c in leaf length) was introduced to account for the case when the theoretical leaf length deviates from the observed leaf length. For most datasets, the estimates of c were greater than zero but less than 10%, indicating that the leaf length predicted by the SGE was usually smaller than the actual length. However, the predicted leaf areas approximated their actual values after considering the floating ratios in leaf length. For most datasets, the mean percent errors of leaf areas were lower than 6%, except for a pooled dataset with 42 bamboo species. For the elliptical, lanceolate, linear, obovate, and ovate shapes, although the SGE did not fit the leaf edge perfectly, after adjusting the parameter c, there were small deviations of the predicted leaf areas from the actual values. This illustrates that leaves with different shapes might have similar functional features for photosynthesis, since the leaf areas can be described by the same equation. The anisotropy expressed as a difference in leaf shape for some plants might be an adaptive response to enable them to adapt to different habitats.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.3390/F9110714
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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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“Why does not the leaf weight-area allometry of bamboos follow the 3/2-power law?”.Lin S, Shao L, Hui C, Song Y, Reddy GVP, Gielis J, Li F, Ding Y, Wei Q, Shi P, Reddy GVP, Frontiers in plant science 9, 583 (2018). http://doi.org/10.3389/FPLS.2018.00583
Abstract: The principle of similarity (Thompson, 1917) states that the weight of an organism follows the 3/2-power law of its surface area and is proportional to its volume on the condition that the density is constant. However, the allometric relationship between leaf weight and leaf area has been reported to greatly deviate from the 3/2-power law, with the irregularity of leaf density largely ignored for explaining this deviation. Here, we choose 11 bamboo species to explore the allometric relationships among leaf area (A), density (ρ), length (L), thickness (T), and weight (W). Because the edge of a bamboo leaf follows a simplified two-parameter Gielis equation, we could show that A ∝ L2 and that A ∝ T2. This then allowed us to derive the density-thickness allometry ρ ∝ Tb and the weight-area allometry W ∝ A(b+3)/2 ≈ A9/8, where b approximates −3/4. Leaf density is strikingly negatively associated with leaf thickness, and it is this inverse relationship that results in the weight-area allometry to deviate from the 3/2-power law. In conclusion, although plants are prone to invest less dry mass and thus produce thinner leaves when the leaf area is sufficient for photosynthesis, such leaf thinning needs to be accompanied with elevated density to ensure structural stability. The findings provide the insights on the evolutionary clue about the biomass investment and output of photosynthetic organs of plants. Because of the importance of leaves, plants could have enhanced the ratio of dry material per unit area of leaf in order to increase the efficiency of photosynthesis, relative the other parts of plants. Although the conclusion is drawn only based on 11 bamboo species, it should also be applicable to the other plants, especially considering previous works on the exponent of the weight-area relationship being less than 3/2 in plants.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.3389/FPLS.2018.00583
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“Application of Gielis transformation to the design of metamaterial structures”. de Jong van Coevorden CM, Gielis J, Caratelli D, Journal of physics : conference series 963, Unsp 012008 (2018). http://doi.org/10.1088/1742-6596/963/1/012008
Abstract: In this communication, the use of Gielis transformation to design more compact metamaterial unit cells is explored. For this purpose, transformed complementary split ring resonators and spiral resonators are coupled to micro-strip lines and theirbehaviour is investigated. The obtained results confirm that the useof the considered class of supershaped geometries enables the synthesis of very compact scalable microwave components.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1088/1742-6596/963/1/012008
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“Modeling of electroporation induced by pulsed electric fields in irregularly shaped cells”. Mescia L, Chiapperino MA, Bia P, Gielis J, Caratelli D, IEEE transactions on biomedical engineering 65, 414 (2018). http://doi.org/10.1109/TBME.2017.2771943
Abstract: During the past decades, the poration of cell membrane induced by pulsed electric fields has been widely investigated. Since the basic mechanisms of this process have not yet been fully clarified, many research activities are focused on the development of suitable theoretical and numerical models. To this end, a nonlinear, nonlocal, dispersive, and space-time numerical algorithm has been developed and adopted to evaluate the transmembrane voltage and pore density along the perimeter of realistic irregularly shaped cells. The presented model is based on the Maxwell's equations and the asymptotic Smoluchowski's equation describing the pore dynamics. The dielectric dispersion of the media forming the cell has been modeled by using a general multirelaxation Debye-based formulation. The irregular shape of the cell is described by using the Gielis' superformula. Different test cases pertaining to red blood cells, muscular cells, cell in mitosis phase, and cancer-like cell have been investigated. For each type of cell, the influence of the relevant shape, the dielectric properties, and the external electric pulse characteristics on the electroporation process has been analyzed. The numerical results demonstrate that the proposed model is an efficient numerical tool to study the electroporation problem in arbitrary-shaped cells.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1109/TBME.2017.2771943
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“The process of cutting GMLmn bodies with dm-knives”. Tavkhelidze I, Gielis J, Sn –, 1512-0066 32, 67 (2018)
Keywords: A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
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“Diatom frustule morphogenesis and function : a multidisciplinary survey”. De Tommasi E, Gielis J, Rogato A, Marine Genomics 35, 1 (2017). http://doi.org/10.1016/J.MARGEN.2017.07.001
Abstract: Diatoms represent the major component of phytoplankton and are responsible for about 2025% of global primary production. Hundreds of millions of years of evolution led to tens of thousands of species differing in dimensions and morphologies. In particular, diatom porous silica cell walls, the frustules, are characterized by an extraordinary, species-specific diversity. It is of great interest, among the marine biologists and geneticists community, to shed light on the origin and evolutionary advantage of this variability of dimensions, geometries and pore distributions. In the present article the main reported data related to frustule morphogenesis and functionalities with contributions from fundamental biology, genetics, mathematics, geometry and physics are reviewed.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1016/J.MARGEN.2017.07.001
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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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“Potential fields of self intersecting Gielis curves for modeling and generalized blending techniques”. Fougerolle Y, Truchetet F, Gielis J, Modeling In Mathematics 2, 67 (2017). http://doi.org/10.2991/978-94-6239-261-8_6
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[.
Keywords: P1 Proceeding; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.2991/978-94-6239-261-8_6
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“On a geometric model of bodies with “complex” configuration and some movements”. Tavkhelidze I, Caratelli D, Gielis J, Ricci PE, Rogava M, Transirico M page 129 (2017).
Abstract: Aim of this chapter is analytical representation of one wide class of geometric figures (lines, surfaces and bodies) and their complicated displacements. The accurate estimation of physical characteristics (such as volume, surface area, length, or other specific parameters) relevant to human organs is of fundamental importance in medicine. One central idea of this article is, in this respect, to provide a general methodology for the evaluation, as a function of time, of the volume and center of gravity featured by moving of one class of bodies used of describe different human organs.
Keywords: H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.2991/978-94-6239-261-8_10
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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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“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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“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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“A geometrical model for testing bilateral symmetry of bamboo leaf with a simplified Gielis equation”. Lin S, Zhang L, Reddy GVP, Hui C, Gielis J, Ding Y, Shi P, Ecology and evolution 6, 6798 (2016). http://doi.org/10.1002/ECE3.2407
Abstract: The size and shape of plant leaves change with growth, and an accurate description of leaf shape is crucial for describing plant morphogenesis and development. Bilateral symmetry, which has been widely observed but poorly examined, occurs in both dicot and monocot leaves, including all nominated bamboo species (approximately 1,300 species), of which at least 500 are found in China. Although there are apparent differences in leaf size among bamboo species due to genetic and environmental profiles, bamboo leaves have bilateral symmetry with parallel venation and appear similar across species. Here, we investigate whether the shape of bamboo leaves can be accurately described by a simplified Gielis equation, which consists of only two parameters (leaf length and shape) and produces a perfect bilateral shape. To test the applicability of this equation and the occurrence of bilateral symmetry, we first measured the leaf length of 42 bamboo species, examining >500 leaves per species. We then scanned 30 leaves per species that had approximately the same length as the median leaf length for that species. The leaf-shape data from scanned profiles were fitted to the simplified Gielis equation. Results confirmed that the equation fits the leaf-shape data extremely well, with the coefficients of determination being 0.995 on average. We further demonstrated the bilateral symmetry of bamboo leaves, with a clearly defined leaf-shape parameter of all 42 bamboo species investigated ranging from 0.02 to 0.1. This results in a simple and reliable tool for precise determination of bamboo species, with applications in forestry, ecology, and taxonomy.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1002/ECE3.2407
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“Some properties of “bulky&rdquo, links, generated by Generalized Möbius Listing's bodies GML4n”. Caratelli D, Gielis J, Ricci PE, Tavkhelidze I, Journal of mathematical sciences 216, 509 (2016). http://doi.org/10.1007/S10958-016-2907-X
Abstract: In the present paper, we consider the bulky knots and bulky links that appear after cutting of generalized MöbiusListing GML 4 n bodies (with corresponding radial cross sections square) along different generalized MöbiusListing surfaces GML 2 n situated in it. The aim of this article is to examine the number and geometric structure of independent objects that appear after such a cutting process of GML 4 n bodies. In most cases, we are able to count the indices of the resulting mathematical objects according to the known tabulation for knots and links of small complexity.
Keywords: A2 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1007/S10958-016-2907-X
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“Electromagnetic mathematical modeling of 3D supershaped dielectric lens antennas”. Mescia L, Bia P, Caratelli D, Chiapperino MA, Stukach O, Gielis J, Mathematical problems in engineering: theory, methods, and applications , 8130160 (2016). http://doi.org/10.1155/2016/8130160
Abstract: The electromagnetic analysis of a special class of 3D dielectric lens antennas is described in detail. This new class of lens antennas has a geometrical shape defined by the three-dimensional extension of Gielis formula. The analytical description of the lens shape allows the development of a dedicated semianalytical hybrid modeling approach based on geometrical tube tracing and physical optic. In order to increase the accuracy of the model, the multiple reflections occurring within the lens are also taken into account.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1155/2016/8130160
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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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“Comparison of dwarf bamboos (Indocalamus sp.) leaf parameters to determine relationship between spatial density of plants and total leaf area per plant”. Shi P-J, Xu Q, Sandhu HS, Gielis J, Ding Y-L, Li H-R, Dong X-B, Ecology and evolution 5, 4578 (2015). http://doi.org/10.1002/ECE3.1728
Abstract: The relationship between spatial density and size of plants is an important topic in plant ecology. The self-thinning rule suggests a −3/2 power between average biomass and density or a −1/2 power between stand yield and density. However, the self-thinning rule based on total leaf area per plant and density of plants has been neglected presumably because of the lack of a method that can accurately estimate the total leaf area per plant. We aimed to find the relationship between spatial density of plants and total leaf area per plant. We also attempted to provide a novel model for accurately describing the leaf shape of bamboos. We proposed a simplified Gielis equation with only two parameters to describe the leaf shape of bamboos one model parameter represented the overall ratio of leaf width to leaf length. Using this method, we compared some leaf parameters (leaf shape, number of leaves per plant, ratio of total leaf weight to aboveground weight per plant, and total leaf area per plant) of four bamboo species of genus Indocalamus Nakai (I. pedalis (Keng) P.C. Keng, I. pumilus Q.H. Dai and C.F. Keng, I. barbatus McClure, and I. victorialis P.C. Keng). We also explored the possible correlation between spatial density and total leaf area per plant using log-linear regression. We found that the simplified Gielis equation fit the leaf shape of four bamboo species very well. Although all these four species belonged to the same genus, there were still significant differences in leaf shape. Significant differences also existed in leaf area per plant, ratio of leaf weight to aboveground weight per plant, and leaf length. In addition, we found that the total leaf area per plant decreased with increased spatial density. Therefore, we directly demonstrated the self-thinning rule to improve light interception.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1002/ECE3.1728
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“Analysis and synthesis of supershaped dielectric lens antennas”. Bia P, Caratelli D, Mescia L, Gielis J, IET microwaves, antennas and propagation 9, 1497 (2015). http://doi.org/10.1049/IET-MAP.2015.0091
Abstract: A novel class of supershaped dielectric lens antennas, whose geometry is described by the three-dimensional (3D) Gielis formula, is introduced and analysed. To this end, a hybrid modelling approach based on geometrical and physical optics is adopted in order to efficiently analyse the multiple wave reflections occurring within the lens and to evaluate the relevant impact on the radiation properties of the antenna under analysis. The developed modelling procedure has been validated by comparison with numerical results already reported in the literature and, afterwards, applied to the electromagnetic characterisation of Gielis dielectric lens antennas with shaped radiation pattern. Furthermore, a dedicated optimisation algorithm based on quantum particle swarm optimisation has been developed for the synthesis of 3D supershaped lens antennas with single feed, as well as with beamforming capabilities.
Keywords: A1 Journal article; Engineering sciences. Technology; Mass communications; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1049/IET-MAP.2015.0091
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“On means, polynomials and special functions”. Gielis J, Verhulst R, Caratelli D, Ricci PE, Tavkhelidze I, The teaching of mathematics 17, 1 (2014)
Keywords: A1 Journal article; Educational sciences; Sustainable Energy, Air and Water Technology (DuEL)
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“Fourier-Hankel solution of the Robin problem for the Helmholtz equation in supershaped annular domains”. Caratelli D, Gielis J, Tavkhelidze I, Ricci PE, Boundary value problems , 253 (2013). http://doi.org/10.1186/1687-2770-2013-253
Abstract: The Robin problem for the Helmholtz equation in normal-polar annuli is addressed by using a suitable Fourier-Hankel series technique. Attention is in particular focused on the wide class of domains whose boundaries are defined by the so-called superformula introduced by Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica© is developed in order to validate the proposed methodology. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1186/1687-2770-2013-253
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“About “bulky&rdquo, links generated by generalized Möbius-Listing bodies GML2n”. Gielis J, Tavkhelidze I, Ricci PE, Journal of mathematical sciences 193, 449 (2013). http://doi.org/10.1007/S10958-013-1474-7
Abstract: In this paper, we consider the bulky knots and bulky links, which appear after cutting of a Generalized MöbiusListing GMLn2 body (with the radial cross section a convex plane 2-symmetric figure with two vertices) along a different Generalized MöbiusListing surfaces GMLn2 situated in it. The aim of this report is to investigate the number and geometric structure of the independent objects that appear after such a cutting process of GMLn2 bodies. In most cases we are able to count the indices of the resulting mathematical objects according to the known classification for the standard knots and links.
Keywords: A2 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1007/S10958-013-1474-7
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“The Dirichlet problem for the Laplace equation in supershaped annuli”. Caratelli D, Gielis J, Tavkhelidze I, Ricci PE, Boundary value problems , 113 (2013). http://doi.org/10.1186/1687-2770-2013-113
Abstract: The Dirichlet problem for the Laplace equation in normal-polar annuli is addressed by using a suitable Fourier-like technique. Attention is in particular focused on the wide class of domains whose boundaries are defined by the so-called superformula introduced by Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica© is developed in order to validate the proposed methodology. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1186/1687-2770-2013-113
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“About “bulky&rdquo, links, generated by generalized Möbius Listing's bodies GML3n”. Tavkhelidze I, Cassisa C, Gielis J, Ricci PE, Matematica e applicazioni : atti della Accademia nazionale dei Lincei 24, 11 (2013). http://doi.org/10.4171/RLM/643
Abstract: In the present paper we consider the “bulky knots'' and ”bulky links'', which appear after cutting a Generalized Möbius Listing's GMLn3 body (whose radial cross section is a plane 3-symmetric figure with three vertices) along different Generalized Möbius Listing's surfaces GMLn2 situated in it. This article is aimed to investigate the number and geometric structure of the independent objects appearing after such a cutting process of GMLn3 bodies. In most cases we are able to count the indices of the resulting mathematical objects according to the known tabulation for Knots and Links of small complexity.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.4171/RLM/643
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“Spherical harmonic solution of the Robin problem for the Helmholtz equation in a supershaped shell”. Caratelli D, Gielis J, Tavkhelidze I, Ricci PE, Applied mathematics 4, 263 (2013). http://doi.org/10.4236/AM.2013.41A040
Abstract: The Robin problem for the Helmholtz equation in normal-polar shells is addressed by using a suitable spherical harmonic expansion technique. Attention is in particular focused on the wide class of domains whose boundaries are defined by a generalized version of the so-called superformula introduced by Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica? is developed in order to validate the proposed methodology. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.4236/AM.2013.41A040
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“A robust evolutionary algorithm for the recovery of rational Gielis curves”. Fougerolle YD, Truchetet F, Demonceaux C, Gielis J, Pattern recognition 46, 2078 (2013). http://doi.org/10.1016/J.PATCOG.2013.01.024
Abstract: Gielis curves (GC) can represent a wide range of shapes and patterns ranging from star shapes to symmetric and asymmetric polygons, and even self intersecting curves. Such patterns appear in natural objects or phenomena, such as flowers, crystals, pollen structures, animals, or even wave propagation. Gielis curves and surfaces are an extension of Lamé curves and surfaces (superquadrics) which have benefited in the last two decades of extensive researches to retrieve their parameters from various data types, such as range images, 2D and 3D point clouds, etc. Unfortunately, the most efficient techniques for superquadrics recovery, based on deterministic methods, cannot directly be adapted to Gielis curves. Indeed, the different nature of their parameters forbids the use of a unified gradient descent approach, which requires initial pre-processings, such as the symmetry detection, and a reliable pose and scale estimation. Furthermore, even the most recent algorithms in the literature remain extremely sensitive to initialization and often fall into local minima in the presence of large missing data. We present a simple evolutionary algorithm which overcomes most of these issues and unifies all of the required operations into a single though efficient approach. The key ideas in this paper are the replacement of the potential fields used for the cost function (closed form) by the shortest Euclidean distance (SED, iterative approach), the construction of cost functions which minimize the shortest distance as well as the curve length using R-functions, and slight modifications of the evolutionary operators. We show that the proposed cost function based on SED and R-function offers the best compromise in terms of accuracy, robustness to noise, and missing data.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1016/J.PATCOG.2013.01.024
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“Some properties of “bulky&rdquo, links, generated by Generalized Möbius Listing's bodies GML4n”. Caratelli D, Gielis J, Ricci PE, Tavkhelidze I, (2013)
Keywords: P3 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
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“Electromagnetic characterization of supershaped lens antennas for high-frequency applications”. Bia P, Caratelli D, Mescia L, Gielis J page 1679 (2013).
Keywords: H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
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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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