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Author Yao, W.; Hui, C.; Wang, L.; Wang, J.; Gielis, J.; Shi, P. doi  openurl
  Title Comparison of the performance of two polar equations in describing the geometries of elliptical fruits Type A1 Journal article
  Year 2024 Publication Botany letters Abbreviated Journal  
  Volume Issue Pages  
  Keywords (up) A1 Journal article; Antwerp engineering, PhotoElectroChemistry & Sensing (A-PECS)  
  Abstract In nature, the two-dimensional (2D) profiles of fruits from many plants often resemble ellipses. However, it remains unclear whether these profiles strictly adhere to the ellipse equation, as many natural shapes resembling ellipses are actually better described as superellipses. The superellipse equation, which includes an additional parameter n compared to the ellipse equation, can generate a broader range of shapes, with the ellipse being just a special case of the superellipse. To investigate whether the 2D profiles of fruits are better described by ellipses or superellipses, we collected a total of 751 mature and undamaged fruits from 31 naturally growing plants of Cucumis melo L. var. agrestis Naud. Our analysis revealed that most adjusted root-mean-square errors (> 92% of the 751 fruits) for fitting the superellipse equation to the fruit profiles were consistently less than 0.0165. Furthermore, there were 638 of the 751 fruits (ca. 85%) with the 95% confidence intervals of the estimated parameter n in the superellipse equation not including 2. These findings suggest that the profiles of C. melo var. agrestis fruits align more closely with the superellipse equation than with the ellipse equation. This study provides evidence for the existence of the superellipse in fruit profiles, which has significant implications for studying fruit geometries and estimating fruit volumes using the solid of revolution formula. Furthermore, this discovery may contribute to a deeper understanding of the mechanisms driving the evolution of fruit shapes.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 001219634500001 Publication Date 2024-05-08  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 2381-8107; 2381-8115 ISBN Additional Links UA library record; WoS full record  
  Impact Factor 1.5 Times cited Open Access  
  Notes Approved Most recent IF: 1.5; 2024 IF: NA  
  Call Number UA @ admin @ c:irua:205955 Serial 9140  
Permanent link to this record
 

 
Author Gielis, J.; Verhulst, R.; Caratelli, D.; Ricci, P.E.; Tavkhelidze, I. url  openurl
  Title On means, polynomials and special functions Type A1 Journal article
  Year 2014 Publication The teaching of mathematics Abbreviated Journal  
  Volume 17 Issue 1 Pages 1-20  
  Keywords (up) A1 Journal article; Educational sciences; Sustainable Energy, Air and Water Technology (DuEL)  
  Abstract  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos Publication Date  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1451-4966; 2406-1077 ISBN Additional Links UA library record  
  Impact Factor Times cited Open Access  
  Notes Approved no  
  Call Number UA @ admin @ c:irua:128660 Serial 8327  
Permanent link to this record
 

 
Author Bia, P.; Caratelli, D.; Mescia, L.; Gielis, J. pdf  url
doi  openurl
  Title Analysis and synthesis of supershaped dielectric lens antennas Type A1 Journal article
  Year 2015 Publication IET microwaves, antennas and propagation Abbreviated Journal  
  Volume 9 Issue 14 Pages 1497-1504  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Mass communications; Sustainable Energy, Air and Water Technology (DuEL)  
  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.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000364491200002 Publication Date 2015-08-14  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1751-8725 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor Times cited Open Access  
  Notes Approved no  
  Call Number UA @ admin @ c:irua:128659 Serial 7441  
Permanent link to this record
 

 
Author Tian, F.; Wang, Y.; Sandhu, H.S.; Gielis, J.; Shi, P. pdf  url
doi  openurl
  Title Comparison of seed morphology of two ginkgo cultivars Type A1 Journal article
  Year 2020 Publication Journal Of Forestry Research Abbreviated Journal J Forestry Res  
  Volume 31 Issue 3 Pages 751-758  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  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.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000529367600005 Publication Date 2018-07-28  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1007-662x ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 3 Times cited 3 Open Access  
  Notes ; ; Approved Most recent IF: 3; 2020 IF: 0.774  
  Call Number UA @ admin @ c:irua:154987 Serial 6474  
Permanent link to this record
 

 
Author Shi, P.; Ratkowsky, D.A.; Gielis, J. url  doi
openurl 
  Title The generalized Gielis geometric equation and its application Type A1 Journal article
  Year 2020 Publication Symmetry-Basel Abbreviated Journal Symmetry-Basel  
  Volume 12 Issue 4 Pages 645-10  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  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.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000540222200156 Publication Date 2020-04-21  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 2073-8994 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 2.7 Times cited 4 Open Access  
  Notes ; This research was funded by the Jiangsu Government Scholarship for Overseas Studies (grant number: JS-2018-038). ; Approved Most recent IF: 2.7; 2020 IF: 1.457  
  Call Number UA @ admin @ c:irua:168141 Serial 6526  
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Author Shi, P.; Gielis, J.; Quinn, B.K.; Niklas, K.J.; Ratkowsky, D.A.; Schrader, J.; Ruan, H.; Wang, L.; Niinemets, Ü.; Niinennets, U. url  doi
openurl 
  Title ‘biogeom’ : an R package for simulating and fitting natural shapes Type A1 Journal article
  Year 2022 Publication Annals of the New York Academy of Sciences Abbreviated Journal Ann Ny Acad Sci  
  Volume 1516 Issue 1 Pages 123-134  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  Abstract Many natural objects exhibit radial or axial symmetry in a single plane. However, a universal tool for simulating and fitting the shapes of such objects is lacking. Herein, we present an R package called 'biogeom' that simulates and fits many shapes found in nature. The package incorporates novel universal parametric equations that generate the profiles of bird eggs, flowers, linear and lanceolate leaves, seeds, starfish, and tree-rings, and three growth-rate equations that generate the profiles of ovate leaves and the ontogenetic growth curves of animals and plants. 'biogeom' includes several empirical datasets comprising the boundary coordinates of bird eggs, fruits, lanceolate and ovate leaves, tree rings, seeds, and sea stars. The package can also be applied to other kinds of natural shapes similar to those in the datasets. In addition, the package includes sigmoid curves derived from the three growth-rate equations, which can be used to model animal and plant growth trajectories and predict the times associated with maximum growth rate. 'biogeom' can quantify the intra- or interspecific similarity of natural outlines, and it provides quantitative information of shape and ontogenetic modification of shape with important ecological and evolutionary implications for the growth and form of the living world.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000829772300001 Publication Date 2022-07-26  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0077-8923; 1749-6632 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 5.2 Times cited Open Access OpenAccess  
  Notes Approved Most recent IF: 5.2  
  Call Number UA @ admin @ c:irua:189314 Serial 7131  
Permanent link to this record
 

 
Author Li, Y.; Quinn, B.K.; Gielis, J.; Li, Y.; Shi, P. url  doi
openurl 
  Title Evidence that supertriangles exist in nature from the vertical projections of Koelreuteria paniculata fruit Type A1 Journal article
  Year 2022 Publication Symmetry Abbreviated Journal Symmetry-Basel  
  Volume 14 Issue 1 Pages 23  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  Abstract Many natural radial symmetrical shapes (e.g., sea stars) follow the Gielis equation (GE) or its twin equation (TGE). A supertriangle (three triangles arranged around a central polygon) represents such a shape, but no study has tested whether natural shapes can be represented as/are supertriangles or whether the GE or TGE can describe their shape. We collected 100 pieces of Koelreuteria paniculata fruit, which have a supertriangular shape, extracted the boundary coordinates for their vertical projections, and then fitted them with the GE and TGE. The adjusted root mean square errors (RMSEadj) of the two equations were always less than 0.08, and >70% were less than 0.05. For 57/100 fruit projections, the GE had a lower RMSEadj than the TGE, although overall differences in the goodness of fit were non-significant. However, the TGE produces more symmetrical shapes than the GE as the two parameters controlling the extent of symmetry in it are approximately equal. This work demonstrates that natural supertriangles exist, validates the use of the GE and TGE to model their shapes, and suggests that different complex radially symmetrical shapes can be generated by the same equation, implying that different types of biological symmetry may result from the same biophysical mechanisms.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000746030100001 Publication Date 2021-12-27  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 2073-8994 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 2.7 Times cited Open Access OpenAccess  
  Notes Approved Most recent IF: 2.7  
  Call Number UA @ admin @ c:irua:186453 Serial 7158  
Permanent link to this record
 

 
Author Wang, L.; Miao, Q.; Niinemets, Ü.; Gielis, J.; Shi, P. url  doi
openurl 
  Title Quantifying the variation in the geometries of the outer rims of corolla tubes of Vinca major L Type A1 Journal article
  Year 2022 Publication Plants Abbreviated Journal  
  Volume 11 Issue 15 Pages 1987-12  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  Abstract Many geometries of plant organs can be described by the Gielis equation, a polar coordinate equation extended from the superellipse equation, . Here, r is the polar radius corresponding to the polar angle φ; m is a positive integer that determines the number of angles of the Gielis curve when φ ∈ [0 to 2π); and the rest of the symbols are parameters to be estimated. The pentagonal radial symmetry of calyxes and corolla tubes in top view is a common feature in the flowers of many eudicots. However, prior studies have not tested whether the Gielis equation can depict the shapes of corolla tubes. We sampled randomly 366 flowers of Vinca major L., among which 360 had five petals and pentagonal corolla tubes, and six had four petals and quadrangular corolla tubes. We extracted the planar coordinates of the outer rims of corolla tubes (in top view) (ORCTs), and then fitted the data with two simplified versions of the Gielis equation with k = 1 and m = 5: (Model 1), and (Model 2). The adjusted root mean square error (RMSEadj) was used to evaluate the goodness of fit of each model. In addition, to test whether ORCTs are radially symmetrical, we correlated the estimates of n2 and n3 in Model 1 on a log-log scale. The results validated the two simplified Gielis equations. The RMSEadj values for all corolla tubes were smaller than 0.05 for both models. The numerical values of n2 and n3 were demonstrated to be statistically equal based on the regression analysis, which suggested that the ORCTs of V. major are radially symmetrical. It suggests that Model 1 can be replaced by the simpler Model 2 for fitting the ORCT in this species. This work indicates that the pentagonal or quadrangular corolla tubes (in top view) can both be modeled by the Gielis equation and demonstrates that the pentagonal or quadrangular corolla tubes of plants tend to form radial symmetrical geometries during their development and growth.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000839115100001 Publication Date 2022-08-01  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 2223-7747 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor Times cited Open Access OpenAccess  
  Notes Approved Most recent IF: NA  
  Call Number UA @ admin @ c:irua:189315 Serial 7200  
Permanent link to this record
 

 
Author Shi, P.; Wang, L.; Quinn, B.K.K.; Gielis, J. url  doi
openurl 
  Title A new program to estimate the parameters of Preston's equation, a general formula for describing the egg shape of birds Type A1 Journal article
  Year 2023 Publication Symmetry Abbreviated Journal Symmetry-Basel  
  Volume 15 Issue 1 Pages 231-10  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  Abstract Preston's equation is a general model describing the egg shape of birds. The parameters of Preston's equation are usually estimated after re-expressing it as the Todd-Smart equation and scaling the egg's actual length to two. This method assumes that the straight line through the two points on an egg's profile separated by the maximum distance (i.e., the longest axis of an egg's profile) is the mid-line. It hypothesizes that the photographed egg's profile is perfectly bilaterally symmetrical, which seldom holds true because of photographic errors and placement errors. The existing parameter estimation method for Preston's equation considers an angle of deviation for the longest axis of an egg's profile from the mid-line, which decreases prediction errors to a certain degree. Nevertheless, this method cannot provide an accurate estimate of the coordinates of the egg's center, and it leads to sub-optimal parameter estimation. Thus, it is better to account for the possible asymmetry between the two sides of an egg's profile along its mid-line when fitting egg-shape data. In this paper, we propose a method based on the optimization algorithm (optimPE) to fit egg-shape data and better estimate the parameters of Preston's equation by automatically searching for the optimal mid-line of an egg's profile and testing its validity using profiles of 59 bird eggs spanning a wide range of existing egg shapes. We further compared this method with the existing one based on multiple linear regression (lmPE). This study demonstrated the ability of the optimPE method to estimate numerical values of the parameters of Preston's equation and provide the theoretical egg length (i.e., the distance between two ends of the mid-line of an egg's profile) and the egg's maximum breadth. This provides a valuable approach for comparing egg shapes among conspecifics or across different species, or even different classes (e.g., birds and reptiles), in future investigations.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000927531000001 Publication Date 2023-01-13  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 2073-8994 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 2.7 Times cited Open Access OpenAccess  
  Notes Approved Most recent IF: 2.7; 2023 IF: 1.457  
  Call Number UA @ admin @ c:irua:195347 Serial 7279  
Permanent link to this record
 

 
Author Wang, L.; Ratkowsky, D.A.; Gielis, J.; Ricci, P.E.; Shi, P. url  doi
openurl 
  Title Effects of the numerical values of the parameters in the Gielis equation on its geometries Type A1 Journal article
  Year 2022 Publication Symmetry Abbreviated Journal Symmetry-Basel  
  Volume 14 Issue 12 Pages 2475-12  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  Abstract The Lamé curve is an extension of an ellipse, the latter being a special case. Dr. Johan Gielis further extended the Lamé curve in the polar coordinate system by introducing additional parameters (n1, n2, n3; m): rφ=1Acosm4φn2+1Bsinm4φn3−1/n1, which can be applied to model natural geometries. Here, r is the polar radius corresponding to the polar angle φ; A, B, n1, n2 and n3 are parameters to be estimated; m is the positive real number that determines the number of angles of the Gielis curve. Most prior studies on the Gielis equation focused mainly on its applications. However, the Gielis equation can also generate a large number of shapes that are rotationally symmetric and axisymmetric when A = B and n2 = n3, interrelated with the parameter m, with the parameters n1 and n2 determining the shapes of the curves. In this paper, we prove the relationship between m and the rotational symmetry and axial symmetry of the Gielis curve from a theoretical point of view with the condition A = B, n2 = n3. We also set n1 and n2 to take negative real numbers rather than only taking positive real numbers, then classify the curves based on extremal properties of r(φ) at φ = 0, π/m when n1 and n2 are in different intervals, and analyze how n1, n2 precisely affect the shapes of Gielis curves.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000904525700001 Publication Date 2022-11-23  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 2073-8994 ISBN Additional Links UA library record; WoS full record  
  Impact Factor 2.7 Times cited Open Access OpenAccess  
  Notes Approved Most recent IF: 2.7  
  Call Number UA @ admin @ c:irua:191860 Serial 7301  
Permanent link to this record
 

 
Author Tavkhelidze, I.; Cassisa, C.; Gielis, J.; Ricci, P.E. pdf  doi
openurl 
  Title About “bulky” links, generated by generalized Möbius Listing's bodies GML3n Type A1 Journal article
  Year 2013 Publication Matematica e applicazioni : atti della Accademia nazionale dei Lincei Abbreviated Journal  
  Volume 24 Issue 1 Pages 11-38  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  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.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000316567700002 Publication Date 2013-03-13  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1120-6357 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor Times cited Open Access  
  Notes Approved no  
  Call Number UA @ admin @ c:irua:107174 Serial 7405  
Permanent link to this record
 

 
Author de Jong van Coevorden, C.M.; Gielis, J.; Caratelli, D. url  doi
openurl 
  Title Application of Gielis transformation to the design of metamaterial structures Type A1 Journal article
  Year 2018 Publication Journal of physics : conference series Abbreviated Journal  
  Volume 963 Issue Pages Unsp 012008  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  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.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000435022800008 Publication Date 2018-02-20  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1742-6588; 1742-6596 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor Times cited Open Access  
  Notes Approved no  
  Call Number UA @ admin @ c:irua:150947 Serial 7475  
Permanent link to this record
 

 
Author Shi, P.-J.; Xu, Q.; Sandhu, H.S.; Gielis, J.; Ding, Y.-L.; Li, H.-R.; Dong, X.-B. url  doi
openurl 
  Title Comparison of dwarf bamboos (Indocalamus sp.) leaf parameters to determine relationship between spatial density of plants and total leaf area per plant Type A1 Journal article
  Year 2015 Publication Ecology and evolution Abbreviated Journal  
  Volume 5 Issue 20 Pages 4578-4589  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  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.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000363731500008 Publication Date 2015-09-30  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 2045-7758 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor Times cited Open Access  
  Notes Approved no  
  Call Number UA @ admin @ c:irua:128662 Serial 7691  
Permanent link to this record
 

 
Author Mescia, L.; Chiapperino, M.A.; Bia, P.; Lamacchia, C.M.; Gielis, J.; Caratelli, D. url  doi
openurl 
  Title Design of electroporation process in irregularly shaped multicellular systems Type A1 Journal article
  Year 2019 Publication Electronics (Basel) Abbreviated Journal  
  Volume 8 Issue 1 Pages 37  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  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.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000457142800037 Publication Date 2019-01-03  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 2079-9292 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor Times cited Open Access  
  Notes Approved no  
  Call Number UA @ admin @ c:irua:157203 Serial 7765  
Permanent link to this record
 

 
Author De Tommasi, E.; Gielis, J.; Rogato, A. pdf  url
doi  openurl
  Title Diatom frustule morphogenesis and function : a multidisciplinary survey Type A1 Journal article
  Year 2017 Publication Marine Genomics Abbreviated Journal  
  Volume 35 Issue Pages 1-18  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  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.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000412957700001 Publication Date 2017-07-20  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1874-7787 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor Times cited Open Access  
  Notes Approved no  
  Call Number UA @ admin @ c:irua:144546 Serial 7807  
Permanent link to this record
 

 
Author Caratelli, D.; Gielis, J.; Tavkhelidze, I.; Ricci, P.E. url  doi
openurl 
  Title The Dirichlet problem for the Laplace equation in supershaped annuli Type A1 Journal article
  Year 2013 Publication Boundary value problems Abbreviated Journal  
  Volume Issue Pages 113-10  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  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.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000325760900002&DestLinkType=CitingArticles&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7 Publication Date 2013-05-03  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1687-2762; 1687-2770 ISBN Additional Links UA library record; WoS citing articles; WoS full record  
  Impact Factor Times cited Open Access  
  Notes Approved no  
  Call Number UA @ admin @ c:irua:108644 Serial 7812  
Permanent link to this record
 

 
Author Mescia, L.; Bia, P.; Caratelli, D.; Chiapperino, M.A.; Stukach, O.; Gielis, J. url  doi
openurl 
  Title Electromagnetic mathematical modeling of 3D supershaped dielectric lens antennas Type A1 Journal article
  Year 2016 Publication Mathematical problems in engineering: theory, methods, and applications Abbreviated Journal  
  Volume Issue Pages 8130160-10  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  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.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000372246600001 Publication Date 2016-02-29  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1024-123x; 1563-5147 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor Times cited Open Access  
  Notes Approved no  
  Call Number UA @ admin @ c:irua:131516 Serial 7866  
Permanent link to this record
 

 
Author Martínez-Dueñas, E.J.R.; de Jong van Coevorden, C.M.; Stukach, O.V.; Panokin, N.V.; Gielis, J.; Caratelli, D. url  doi
openurl 
  Title Electromagnetic modeling and design of a novel class of complementary split‐ring resonators Type A1 Journal article
  Year 2019 Publication International journal of RF and microwave computer-aided engineering Abbreviated Journal  
  Volume 29 Issue 4 Pages e21582  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  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.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000460308500020 Publication Date 2018-11-19  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1096-4290 ISBN Additional Links UA library record; WoS full record  
  Impact Factor Times cited Open Access  
  Notes Approved no  
  Call Number UA @ admin @ c:irua:155021 Serial 7867  
Permanent link to this record
 

 
Author Caratelli, D.; Gielis, J.; Tavkhelidze, I.; Ricci, P.E. url  doi
openurl 
  Title Fourier-Hankel solution of the Robin problem for the Helmholtz equation in supershaped annular domains Type A1 Journal article
  Year 2013 Publication Boundary value problems Abbreviated Journal  
  Volume Issue Pages 253  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  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.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000340237600004 Publication Date 2013-11-22  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1687-2762; 1687-2770 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor Times cited Open Access  
  Notes Approved no  
  Call Number UA @ admin @ c:irua:111558 Serial 7981  
Permanent link to this record
 

 
Author Gielis, J.; Tavkhelidze, I. url  doi
openurl 
  Title The general case of cutting of Generalized Möbius-Listing surfaces and bodies Type A1 Journal article
  Year 2020 Publication 4Open Abbreviated Journal  
  Volume 3 Issue Pages 7-48  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  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.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos Publication Date 2020-08-31  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 2557-0250 ISBN Additional Links UA library record  
  Impact Factor Times cited Open Access  
  Notes Approved Most recent IF: NA  
  Call Number UA @ admin @ c:irua:174471 Serial 7992  
Permanent link to this record
 

 
Author Lin, S.; Zhang, L.; Reddy, G.V.P.; Hui, C.; Gielis, J.; Ding, Y.; Shi, P. url  doi
openurl 
  Title A geometrical model for testing bilateral symmetry of bamboo leaf with a simplified Gielis equation Type A1 Journal article
  Year 2016 Publication Ecology and evolution Abbreviated Journal  
  Volume 6 Issue 19 Pages 6798-6806  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  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.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000385626100003 Publication Date 2016-09-02  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 2045-7758 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor Times cited Open Access  
  Notes Approved no  
  Call Number UA @ admin @ c:irua:144547 Serial 7998  
Permanent link to this record
 

 
Author Shi, P.; Liu, M.; Yu, X.; Gielis, J.; Ratkowsky, D.A. url  doi
openurl 
  Title Proportional relationship between leaf area and the product of leaf length and width of four types of special leaf shapes Type A1 Journal article
  Year 2019 Publication Forests (19994907) Abbreviated Journal  
  Volume 10 Issue 2 Pages 178  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  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.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000460744000102 Publication Date 2019-02-20  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1999-4907 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor Times cited Open Access  
  Notes Approved no  
  Call Number UA @ admin @ c:irua:157200 Serial 8427  
Permanent link to this record
 

 
Author Fougerolle, Y.D.; Truchetet, F.; Demonceaux, C.; Gielis, J. pdf  doi
openurl 
  Title A robust evolutionary algorithm for the recovery of rational Gielis curves Type A1 Journal article
  Year 2013 Publication Pattern recognition Abbreviated Journal  
  Volume 46 Issue 8 Pages 2078-2091  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  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.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000317944800002 Publication Date 2013-01-29  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0031-3203 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor Times cited Open Access  
  Notes Approved no  
  Call Number UA @ admin @ c:irua:107181 Serial 8485  
Permanent link to this record
 

 
Author Huang, W.; Su, X.; Ratkowsky, D.A.; Niklas, K.J.; Gielis, J.; Shi, P. url  doi
openurl 
  Title The scaling relationships of leaf biomass vs. leaf surface area of 12 bamboo species Type A1 Journal article
  Year 2019 Publication Global ecology and conservation Abbreviated Journal  
  Volume 20 Issue Pages e00793  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  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.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000498226800095 Publication Date 2019-09-19  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 2351-9894; 2351-9894 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor Times cited Open Access  
  Notes Approved no  
  Call Number UA @ admin @ c:irua:162954 Serial 8497  
Permanent link to this record
 

 
Author Caratelli, D.; Gielis, J.; Tavkhelidze, I.; Ricci, P.E. url  doi
openurl 
  Title Spherical harmonic solution of the Robin problem for the Helmholtz equation in a supershaped shell Type A1 Journal article
  Year 2013 Publication Applied mathematics Abbreviated Journal  
  Volume 4 Issue 1a Pages 263-270  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  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.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos Publication Date 2013-01-30  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 2152-7385 ISBN Additional Links UA library record  
  Impact Factor Times cited Open Access  
  Notes Approved no  
  Call Number UA @ admin @ c:irua:107177 Serial 8576  
Permanent link to this record
 

 
Author Huang, W.; Li, Y.; Niklas, K.J.; Gielis, J.; Ding, Y.; Cao, L.; Shi, P. url  doi
openurl 
  Title A superellipse with deformation and its application in describing the cross-sectional shapes of a square bamboo Type A1 Journal article
  Year 2020 Publication Symmetry-Basel Abbreviated Journal Symmetry-Basel  
  Volume 12 Issue 12 Pages 2073  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  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.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000602546300001 Publication Date 2020-12-15  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 2073-8994 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 2.7 Times cited Open Access  
  Notes Approved Most recent IF: 2.7; 2020 IF: 1.457  
  Call Number UA @ admin @ c:irua:174472 Serial 8622  
Permanent link to this record
 

 
Author Gielis, J.; Caratelli, D.; Fougerolle, Y.; Ricci, P.E.; Tavkelidze, I.; Gerats, T. url  doi
openurl 
  Title Universal natural shapes : from unifying shape description to simple methods for shape analysis and boundary value problems Type A1 Journal article
  Year 2012 Publication PLoS ONE Abbreviated Journal  
  Volume 7 Issue 9 Pages e29324-11  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  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.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000309517500001 Publication Date 2012-09-30  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1932-6203 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor Times cited Open Access  
  Notes Approved no  
  Call Number UA @ admin @ c:irua:102202 Serial 8711  
Permanent link to this record
 

 
Author Lin, S.; Shao, L.; Hui, C.; Song, Y.; Reddy, G.V.P.; Gielis, J.; Li, F.; Ding, Y.; Wei, Q.; Shi, P.; Reddy, G.V.P. url  doi
openurl 
  Title Why does not the leaf weight-area allometry of bamboos follow the 3/2-power law? Type A1 Journal article
  Year 2018 Publication Frontiers in plant science Abbreviated Journal  
  Volume 9 Issue Pages 583  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  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.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000431415100001 Publication Date 2018-05-04  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1664-462x ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor Times cited Open Access  
  Notes Approved no  
  Call Number UA @ admin @ c:irua:150948 Serial 8758  
Permanent link to this record
 

 
Author Shi, P.; Chen, L.; Quinn, B.K.; Yu, K.; Miao, Q.; Guo, X.; Lian, M.; Gielis, J.; Niklas, K.J. pdf  url
doi  openurl
  Title A simple way to calculate the volume and surface area of avian eggs Type A1 Journal article
  Year 2023 Publication Annals of the New York Academy of Sciences Abbreviated Journal  
  Volume 1524 Issue 1 Pages 118-131  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  Abstract Egg geometry can be described using Preston's equation, which has seldom been used to calculate egg volume (V) and surface area (S) to explore S versus V scaling relationships. Herein, we provide an explicit re-expression of Preston's equation (designated as EPE) to calculate V and S, assuming that an egg is a solid of revolution. The side (longitudinal) profiles of 2221 eggs of six avian species were digitized, and the EPE was used to describe each egg profile. The volumes of 486 eggs from two avian species predicted by the EPE were compared with those obtained using water displacement in graduated cylinders. There was no significant difference in V using the two methods, which verified the utility of the EPE and the hypothesis that eggs are solids of revolution. The data also indicated that V is proportional to the product of egg length (L) and maximum width (W) squared. A 2/3-power scaling relationship between S and V for each species was observed, that is, S is proportional to (LW2)(2/3). These results can be extended to describe the shapes of the eggs of other species to study the evolution of avian (and perhaps reptilian) eggs.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000975679400001 Publication Date 2023-04-28  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0077-8923; 1749-6632 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 5.2 Times cited Open Access OpenAccess  
  Notes Approved Most recent IF: 5.2; 2023 IF: 4.706  
  Call Number UA @ admin @ c:irua:196724 Serial 8827  
Permanent link to this record
 

 
Author Wang, L.; Shi, P.; Chen, L.; Gielis, J.; Niklas, K.J. pdf  url
doi  openurl
  Title Evidence that Chinese white olive (Canarium album(Lour.) DC.) fruits are solids of revolution Type A1 Journal article
  Year 2023 Publication Botany letters Abbreviated Journal  
  Volume Issue Pages 1-7  
  Keywords (up) A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  Abstract Although many fruit geometries resemble a solid of revolution, this assumption has rarely been rigorously examined. To test this assumption, 574 fruits of Canarium album (Lour.) DC. which appear to have an ellipsoidal shape, were examined to determine the validity of a general avian-based egg-shape equation, referred to as the explicit Preston equation (EPE). The assumption that the C. album fruit geometry is a solid of revolution is tested by applying the volume formula for a solid of revolution using the EPE. The goodness of fit of the EPE was assessed using the adjusted root-mean-square error (RMSEadj). The relationship between the observed volume (Vobs) of each fruit, as measured by water displacement in a graduated cylinder, and the predicted volumes (Vpre) based on the EPE was also evaluated using the equation Vpre = slope * Vobs. All the RMSEadj values were smaller than 0.05, which demonstrated the validity of the EPE based on C. album fruit profiles. The 95% confidence interval of the slope of Vpre vs. Vobs included 1.0, indicating that there was no significant difference between Vpre and Vobs. The data confirm that C. album fruits are solids of revolution. This study provides a new approach for calculating the volume and surface area of geometrically similar fruits, which can be extended to other species with similar fruit geometries to further explore the ontogeny and evolution of angiosperm reproductive organs.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 001033135400001 Publication Date 2023-07-25  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 2381-8107; 2381-8115 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 1.5 Times cited Open Access Not_Open_Access: Available from 24.01.2024  
  Notes Approved Most recent IF: 1.5; 2023 IF: NA  
  Call Number UA @ admin @ c:irua:198001 Serial 8864  
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