“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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“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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“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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“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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“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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“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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“Design of electroporation process in irregularly shaped multicellular systems”. Mescia L, Chiapperino MA, Bia P, Lamacchia CM, Gielis J, Caratelli D, Electronics (Basel) 8, 37 (2019). http://doi.org/10.3390/ELECTRONICS8010037
Abstract: Electroporation technique is widely used in biotechnology and medicine for the transport of various molecules through the membranes of biological cells. Different mathematical models of electroporation have been proposed in the literature to study pore formation in plasma and nuclear membranes. These studies are mainly based on models using a single isolated cell with a canonical shape. In this work, a spacetime (x,y,t) multiphysics model based on quasi-static Maxwells equations and nonlinear Smoluchowskis equation has been developed to investigate the electroporation phenomenon induced by pulsed electric field in multicellular systems having irregularly shape. The dielectric dispersion of the cell compartments such as nuclear and plasmatic membranes, cytoplasm, nucleoplasm and external medium have been incorporated into the numerical algorithm, too. Moreover, the irregular cell shapes have been modeled by using the Gielis transformations.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.3390/ELECTRONICS8010037
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“Design of irregularly shaped lens antennas including supershaped feed”. Mescia L, Lamacchia CM, Chiapperino MA, Bia P, Gielis J, Caratelli D, Progress in Electromagnetic Research Symposium (PIERS)
T2 –, 2019 PhotonIcs &, Electromagnetics Research Symposium –, Spring (PIERS-Spring), 17-20 June, 2019, Rome, Italy , 169 (2019). http://doi.org/10.1109/PIERS-SPRING46901.2019.9017900
Abstract: A new class of irregularly shaped dielectric lens antennas with a supershaped microstrip antenna feeder is presented and detailed in this work. The surface of the lens antenna and the feeder shape have been modelled by using the three and two-dimensional Gielis formula, respectively. The antenna design has been carried out by integrating an home-made software tool with the CST Microwave Studio®. The radiation properties of the whole antenna system have been evaluated using a dedicated high-frequency technique based on the tube tracing approximation. Moreover, the effects due to the multiple internal reflections have been properly modeled. The proposed model was applied to study unusual and complex lens antenna systems with the aim to design special radiation characteristics.
Keywords: P1 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1109/PIERS-SPRING46901.2019.9017900
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“Electromagnetic modeling and design of a novel class of complementary split‐ring resonators”. Martínez-Dueñas EJR, de Jong van Coevorden CM, Stukach OV, Panokin NV, Gielis J, Caratelli D, International journal of RF and microwave computer-aided engineering 29, e21582 (2019). http://doi.org/10.1002/MMCE.21582
Abstract: This research study reports the assessment of complementary split ring resonators based on Gielis transformation as basic elements for the design of high‐performance microwave components in printed technology. From the electromagnetic simulation of said structures, suitable equivalent circuit models are extracted and analyzed. Physical prototypes are fabricated and tested for design validation. The obtained results confirm that the adoption of supershaped geometries enables the synthesis of very compact scalable microwave filters.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1002/MMCE.21582
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“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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“Leaf area-length allometry and its implications in leaf shape evolution”. Shi P, Liu M, Ratkowsky DA, Gielis J, Su J, Yu X, Wang P, Zhang L, Lin Z, Schrader J, Trees: structure and function 33, 1073 (2019). http://doi.org/10.1007/S00468-019-01843-4
Abstract: According to Thompson’s principle of similarity, the area of an object should be proportional to its length squared. However, leaf area–length data of some plants have been demonstrated not to follow the principle of similarity. We explore the reasons why the leaf area–length allometry deviates from the principle of similarity and examine whether there is a general model describing the relationship among leaf area, width and length. We sampled more than 11,800 leaves from six classes of woody and herbaceous plants and tested the leaf area–length allometry. We compared six mathematical models based on root-mean-square error as the measure of goodness-of-fit. The best supported model described a proportional relationship between leaf area and the product of leaf width and length (i.e., the Montgomery model). We found that the extent to which the leaf area–length allometry deviates from the principle of similarity depends upon the extent of variation of the ratio of leaf width to length. Estimates of the parameter of the Montgomery model ranged between 1/2, which corresponds to a triangular leaf with leaf length as its height and leaf width as its base, and π/4, which corresponds to an elliptical leaf with leaf length as its major axis and leaf width as its minor axis, for the six classes of plants. The narrow range in practice of the Montgomery parameter implies an evolutionary stability for the leaf area of large-leaved plants despite the fact that leaf shapes of these plants are rather different.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1007/S00468-019-01843-4
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“Multiphysics modelling of membrane electroporation in irregularly shaped cells”. Mescia L, Chiapperino MA, Bia P, Lamacchia CM, Gielis J, Caratelli D, Progress in Electromagnetic Research Symposium (PIERS)
T2 –, 2019 PhotonIcs &, Electromagnetics Research Symposium –, Spring (PIERS-Spring), 17-20 June 2019, Rome, Italy , 2992 (2019). http://doi.org/10.1109/PIERS-SPRING46901.2019.9017428
Abstract: Electroporation is a non-thermal electromagnetic phenomenon widely used in medical diseases treatment. Different mathematical models of electroporation have been proposed in literature to study pore evolution in biological membranes. This paper presents a nonlinear dispersive multiphysic model of electroporation in irregular shaped biological cells in which the spatial and temporal evolution of the pores size is taken into account. The model solves Maxwell and asymptotic Smoluchowski equations and it describes the dielectric dispersion of cell media using a Debye-based relationship. Furthermore, the irregular cell shape has been modeled using the Gielis superformula. Taking into account the cell in mitosis phase, the electroporation process has been studied comparing the numerical results pertaining the model with variable pore radius with those in which the pore radius is supposed constant. The numerical analysis has been performed exposing the biological cell to a rectangular electric pulse having duration of 10 μs. The obtained numerical results highlight considerable differences between the two different models underling the need to include into the numerical algorithm the differential equation modeling the spatial and time evolution of the pores size.
Keywords: P1 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1109/PIERS-SPRING46901.2019.9017428
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“Nonlinear dispersive model of electroporation for irregular nucleated cells”. Chiapperino MA, Bia P, Caratelli D, Gielis J, Mescia L, Dermol-Cerne J, Miklavcic D, Bioelectromagnetics 40, 331 (2019). http://doi.org/10.1002/BEM.22197
Abstract: In this work, the electroporation phenomenon induced by pulsed electric field on different nucleated biological cells is studied. A nonlinear, non-local, dispersive, and space-time multiphysics model based on Maxwell's and asymptotic Smoluchowski's equations has been developed to calculate the transmembrane voltage and pore density on both plasma and nuclear membrane perimeters. The irregular cell shape has been modeled by incorporating in the numerical algorithm the analytical functions pertaining to Gielis curves. The dielectric dispersion of the cell media has been modeled considering the multi-relaxation Debye-based relationship. Two different irregular nucleated cells have been investigated and their response has been studied applying both the dispersive and non-dispersive models. By a comparison of the obtained results, differences can be highlighted confirming the need to make use of the dispersive model to effectively investigate the cell response in terms of transmembrane voltages, pore densities, and electroporation opening angle, especially when irregular cell shapes and short electric pulses are considered. Bioelectromagnetics. 2019;40:331-342. (c) 2019 Wiley Periodicals, Inc.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1002/BEM.22197
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“Proportional relationship between leaf area and the product of leaf length and width of four types of special leaf shapes”. Shi P, Liu M, Yu X, Gielis J, Ratkowsky DA, Forests (19994907) 10, 178 (2019). http://doi.org/10.3390/F10020178
Abstract: The leaf area, as an important leaf functional trait, is thought to be related to leaf length and width. Our recent study showed that the Montgomery equation, which assumes that leaf area is proportional to the product of leaf length and width, applied to different leaf shapes, and the coefficient of proportionality (namely the Montgomery parameter) range from 1/2 to π/4. However, no relevant geometrical evidence has previously been provided to support the above findings. Here, four types of representative leaf shapes (the elliptical, sectorial, linear, and triangular shapes) were studied. We derived the range of the estimate of the Montgomery parameter for every type. For the elliptical and triangular leaf shapes, the estimates are π/4 and 1/2, respectively; for the linear leaf shape, especially for the plants of Poaceae that can be described by the simplified Gielis equation, the estimate ranges from 0.6795 to π/4; for the sectorial leaf shape, the estimate ranges from 1/2 to π/4. The estimates based on the observations of actual leaves support the above theoretical results. The results obtained here show that the coefficient of proportionality of leaf area versus the product of leaf length and width only varies in a small range, maintaining the allometric relationship for leaf area and thereby suggesting that the proportional relationship between leaf area and the product of leaf length and width broadly remains stable during leaf evolution.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.3390/F10020178
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“Relevance of the cell membrane modelling for accurate analysis of the pulsed electric field-induced electroporation”. Mescia L, Chiapperino MA, Bia P, Lamacchia CM, Gielis J, Caratelli D, Progress in Electromagnetic Research Symposium (PIERS)
T2 –, 2019 PhotonIcs &, Electromagnetics Research Symposium –, Spring (PIERS-Spring), 17-20 June 2019, Rome, Italy , 2985 (2019). http://doi.org/10.1109/PIERS-SPRING46901.2019.9017456
Abstract: In this work, a nonlinear dispersive multiphysic model based on Maxwell and asymptotic Smoluchowsky equations has been developed to analyze the electroporation phenomenon induced by pulsed electric field on biological cells. The irregular plasma membrane geometry has been modeled by incorporating in the numerical algorithm the Gielis superformula as well as the dielectric dispersion of the plasma membrane has been modeled using the multi-relaxation Debye-based relationship. The study has been carried out with the aim to compare our model implementing a thin plasma membrane with the simplified model in which the plasma membrane is modeled as a distributed impedance boundary condition. The numerical analysis has been performed exposing the cell to external electric pulses having rectangular shapes. By an inspection of the obtained results, significant differences can be highlighted between the two models confirming the need to incorporate the effective thin membrane into the numerical algorithm to well predict the cell response to the pulsed electric fields in terms of transmembrane voltages and pore densities, especially when the cell is exposed to external nanosecond pulses.
Keywords: P1 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1109/PIERS-SPRING46901.2019.9017456
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“The scaling relationships of leaf biomass vs. leaf surface area of 12 bamboo species”. Huang W, Su X, Ratkowsky DA, Niklas KJ, Gielis J, Shi P, Global ecology and conservation 20, e00793 (2019). http://doi.org/10.1016/J.GECCO.2019.E00793
Abstract: There is convincing evidence for a scaling relationship between leaf dry weight (DW) and leaf surface area (A) for broad-leaved plants, and most estimates of the scaling exponent of DW vs. A are greater than unity. However, the scaling relationship of leaf fresh weight (FW) vs. A has been largely neglected. In the present study, we examined whether there is a statistically strong scaling relationship between FW and A and compared the goodness of fit to that of DW vs. A. Between 250 and 520 leaves from each of 12 bamboo species within 2 genera (Phyllostachys and Pleioblastus) were investigated. The reduced major axis regression protocols were used to determine scaling relationships. The fit for the linearized scaling relationship of FW vs. A was compared with that of DW vs. A using the coefficient of determination (i.e., r2). A stronger scaling relationship between FW and A than that between DW and A was observed for each of the 12 bamboo species investigated. Among the 12 species examined, five had significantly smaller scaling exponents of FW vs. A compared to those of DW vs. A; only one species had a scaling exponent of FW vs. A greater than that of DW vs. A. No significant difference between the two scaling exponents was observed for the remaining 6 species. Researchers conducting future studies might be well advised to consider the influence of leaf fresh weight when exploring the scaling relationships of foliar biomass allocation patterns.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1016/J.GECCO.2019.E00793
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“Structure of the dm knives and process of cutting of GML(man) or GRT(man) bodies”. Tavkhelidze I, Gielis J, Sn –, 1512-0066 33 (2019)
Keywords: A3 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
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“Comparison of seed morphology of two ginkgo cultivars”. Tian F, Wang Y, Sandhu HS, Gielis J, Shi P, Journal Of Forestry Research 31, 751 (2020). http://doi.org/10.1007/S11676-018-0770-Y
Abstract: Ginkgo biloba L. is a precious relic tree species with important economic value. Seeds, as a vital reproductive organ of plants, can be used to distinguish cultivars of the species. We chose 400 seeds from two cultivars of ginkgo (Fozhi and Maling; 200 seeds for each cultivar) as the study material and used the Gielis equation to fit the projected shape of these seeds. The coefficients of variation (CV) in root mean squared errors (RMSE) obtained from the fitted data were used to compare the level of inter-cultivar variations in seed shape. We also used the covariance analysis to compare the allometric relationships between seed weights and projected areas of these two cultivars. The Gielis equation fitted well the seed shapes of two ginkgo cultivars. The lower CV in RMSE of cultivar Fozhi than Maling indicated a less symmetrical seed shape in the latter than the former. The bootstrap percentile method showed that the seed shape differences between the two cultivars were significant. However, there was no significant difference in the exponents between the seed weights and the projected areas of these two cultivars. Overall, the significant differences in shapes between the seeds of two ginkgo cultivars were well explained by the Gielis equation; this model can be further extended to compare morphological differences in other ginkgo cultivars, and even for plant seeds or animal eggs that have similar oval shapes.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
Impact Factor: 3
Times cited: 3
DOI: 10.1007/S11676-018-0770-Y
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“The generalized Gielis geometric equation and its application”. Shi P, Ratkowsky DA, Gielis J, Symmetry-Basel 12, 645 (2020). http://doi.org/10.3390/SYM12040645
Abstract: Many natural shapes exhibit surprising symmetry and can be described by the Gielis equation, which has several classical geometric equations (for example, the circle, ellipse and superellipse) as special cases. However, the original Gielis equation cannot reflect some diverse shapes due to limitations of its power-law hypothesis. In the present study, we propose a generalized version by introducing a link function. Thus, the original Gielis equation can be deemed to be a special case of the generalized Gielis equation (GGE) with a power-law link function. The link function can be based on the morphological features of different objects so that the GGE is more flexible in fitting the data of the shape than its original version. The GGE is shown to be valid in depicting the shapes of some starfish and plant leaves.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
Impact Factor: 2.7
Times cited: 4
DOI: 10.3390/SYM12040645
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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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“Parabolic trigonometry”. Dattoli G, Di Palma E, Gielis J, Licciardi S, International journal of applied and computational mathematics 6, 37 (2020). http://doi.org/10.1007/S40819-020-0789-6
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1007/S40819-020-0789-6
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“About some methods of analytic representation and classification of a wide set of geometric figures with “complex&rdquo, configuration”. Tavkhelidze I, Gielis J, Pinelas S, Sn –, 1512-0066 34, 81 (2020)
Keywords: A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
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“About some methods of analytic representation and classification of a wide set of geometric figures with “complex” configuration”. Tavkhelidze I, Gielis J, Pinelas S page 347 (2020).
Keywords: H1 Book chapter; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1007/978-3-030-56323-3_27
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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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“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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“The Mӧbius phenomenon in Generalized Mӧbius-Listing bodies with cross sections of odd and even polygons”. Gielis J, Tavkhelidze I, Sn –, 1512-0066 34, 23 (2020)
Keywords: A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
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“A superellipse with deformation and its application in describing the cross-sectional shapes of a square bamboo”. Huang W, Li Y, Niklas KJ, Gielis J, Ding Y, Cao L, Shi P, Symmetry-Basel 12, 2073 (2020). http://doi.org/10.3390/SYM12122073
Abstract: Many cross-sectional shapes of plants have been found to approximate a superellipse rather than an ellipse. Square bamboos, belonging to the genus Chimonobambusa (Poaceae), are a group of plants with round-edged square-like culm cross sections. The initial application of superellipses to model these culm cross sections has focused on Chimonobambusa quadrangularis (Franceschi) Makino. However, there is a need for large scale empirical data to confirm this hypothesis. In this study, approximately 750 cross sections from 30 culms of C. utilis were scanned to obtain cross-sectional boundary coordinates. A superellipse exhibits a centrosymmetry, but in nature the cross sections of culms usually deviate from a standard circle, ellipse, or superellipse because of the influences of the environment and terrain, resulting in different bending and torsion forces during growth. Thus, more natural cross-sectional shapes appear to have the form of a deformed superellipse. The superellipse equation with a deformation parameter (SEDP) was used to fit boundary data. We find that the cross-sectional shapes (including outer and inner rings) of C. utilis can be well described by SEDP. The adjusted root-mean-square error of SEDP is smaller than that of the superellipse equation without a deformation parameter. A major finding is that the cross-sectional shapes can be divided into two types of superellipse curves: hyperellipses and hypoellipses, even for cross sections from the same culm. There are two proportional relationships between ring area and the product of ring length and width for both the outer and inner rings. The proportionality coefficients are significantly different, as a consequence of the two different superellipse types (i.e., hyperellipses and hypoellipses). The difference in the proportionality coefficients between hyperellipses and hypoellipses for outer rings is greater than that for inner rings. This work informs our understanding and quantifying of the longitudinal deformation of plant stems for future studies to assess the influences of the environment on stem development. This work is also informative for understanding the deviation of natural shapes from a strict rotational symmetry.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
Impact Factor: 2.7
DOI: 10.3390/SYM12122073
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“Can leaf shape be represented by the ratio of leaf width to length? Evidence from nine species of Magnolia and Michelia (Magnoliaceae)”. Shi P, Yu K, Niinemets Ü, Gielis J, Forests 12, 41 (2021). http://doi.org/10.3390/F12010041
Abstract: Leaf shape is closely related to economics of leaf support and leaf functions, including light interception, water use, and CO2 uptake, so correct quantification of leaf shape is helpful for studies of leaf structure/function relationships. There are some extant indices for quantifying leaf shape, including the leaf width/length ratio (W/L), leaf shape fractal dimension (FD), leaf dissection index, leaf roundness index, standardized bilateral symmetrical index, etc. W/L ratio is the simplest to calculate, and recent studies have shown the importance of the W/L ratio in explaining the scaling exponent of leaf dry mass vs. leaf surface area and that of leaf surface area vs. leaf length. Nevertheless, whether the W/L ratio could reflect sufficient geometrical information of leaf shape has been not tested. The FD might be the most accurate measure for the complexity of leaf shape because it can characterize the extent of the self-similarity and other planar geometrical features of leaf shape. However, it is unknown how strongly different indices of leaf shape complexity correlate with each other, especially whether W/L ratio and FD are highly correlated. In this study, the leaves of nine Magnoliaceae species (>140 leaves for each species) were chosen for the study. We calculated the FD value for each leaf using the box-counting approach, and measured leaf fresh mass, surface area, perimeter, length, and width. We found that FD is significantly correlated to the W/L ratio and leaf length. However, the correlation between FD and the W/L ratio was far stronger than that between FD and leaf length for each of the nine species. There were no strong correlations between FD and other leaf characteristics, including leaf area, ratio of leaf perimeter to area, fresh mass, ratio of leaf fresh mass to area, and leaf roundness index. Given the strong correlation between FD and W/L, we suggest that the simpler index, W/L ratio, can provide sufficient information of leaf shape for similarly-shaped leaves. Future studies are needed to characterize the relationships among FD and W/L in leaves with strongly varying shape, e.g., in highly dissected leaves.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
Impact Factor: 1.951
DOI: 10.3390/F12010041
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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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