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Author Caratelli, D.; Gielis, J.; Tavkhelidze, I.; Ricci, P.E.
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 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 (up) Times cited Open Access
Notes Approved no
Call Number UA @ admin @ c:irua:107177 Serial 8576
Permanent link to this record
 
 
Author Tavkhelidze, I.; Gielis, J.
Title Structure of the dm knives and process of cutting of GML(man) or GRT(man) bodies Type A3 Journal article
Year 2019 Publication Sn – 1512-0066 Abbreviated Journal
Volume 33 Issue Pages
Keywords A3 Journal article; Engineering sciences. Technology; 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 ISBN Additional Links UA library record
Impact Factor (up) Times cited Open Access
Notes Approved no
Call Number UA @ admin @ c:irua:164897 Serial 8588
Permanent link to this record
 
 
Author Gielis, J.
Title Temperate bamboos in ornamental horticulture: differentiators and spillover effects into the 21st century Type H3 Book chapter
Year 2012 Publication Abbreviated Journal
Volume Issue Pages 603-623 T2 - Proceedings of the 9th World Bamboo C
Keywords H3 Book chapter; Engineering sciences. Technology; 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 ISBN Additional Links UA library record
Impact Factor (up) Times cited Open Access
Notes Approved no
Call Number UA @ admin @ c:irua:97755 Serial 8644
Permanent link to this record
 
 
Author Gielis, J.; Brasili, S.
Title The apeirogon and dual numbers Type A1 Journal article
Year 2021 Publication Symmetry : culture and science Abbreviated Journal
Volume 32 Issue 2 Pages 157-160
Keywords A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
Abstract The richness, diversity, connection, depth and pleasure of studying symmetry continue to open doors. Here we report a connection between Coxeter's Apeirogon and the geometry associated with pictorial space, parabolic rotation and dual numbers.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Wos 000670122100011 Publication Date 2021-07-02
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0865-4824 ISBN Additional Links UA library record; WoS full record
Impact Factor (up) Times cited Open Access Not_Open_Access
Notes Approved Most recent IF: NA
Call Number UA @ admin @ c:irua:179759 Serial 8652
Permanent link to this record
 
 
Author Caratelli, D.; Gielis, J.; Natalini, P.; Ricci, P.E.; Tavkhelidze, I.
Title The Robin problem for the Helmholtz equation in a starlike planar domain Type A1 Journal article
Year 2011 Publication Georgian mathematical journal Abbreviated Journal
Volume 18 Issue 3 Pages 465-479
Keywords A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
Abstract The interior and exterior Robin problems for the Helmholtz equation in starlike planar domains are addressed by using a suitable Fourier-like technique. Attention is in particular focused on normal-polar domains whose boundaries are defined by the so-called superformula introduced by J. Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica© is developed in order to validate the proposed approach. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained. The computed results are found to be in good agreement with the theoretical findings on Fourier series expansion presented by L. Carleson.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Wos 000296166100004 Publication Date 2021-02-28
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1072-947x ISBN Additional Links UA library record; WoS full record; WoS citing articles
Impact Factor (up) Times cited Open Access
Notes Approved no
Call Number UA @ admin @ c:irua:91086 Serial 8658
Permanent link to this record
 
 
Author Gielis, J.; Ding, Y.; Shi, P.
Title Towards a geometrical theory of morphology and morphogenesis Type P3 Proceeding
Year 2016 Publication Abbreviated Journal
Volume Issue Pages
Keywords P3 Proceeding; Engineering sciences. Technology; 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 ISBN Additional Links UA library record
Impact Factor (up) Times cited Open Access
Notes Approved no
Call Number UA @ admin @ c:irua:144548 Serial 8677
Permanent link to this record
 
 
Author Gielis, J.; Caratelli, D.; Fougerolle, Y.; Ricci, P.E.; Tavkelidze, I.; Gerats, T.
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 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 (up) 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.
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 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 (up) Times cited Open Access
Notes Approved no
Call Number UA @ admin @ c:irua:150948 Serial 8758
Permanent link to this record
 
 
Author Gielis, J.
Title Fred Van Oystaeyen : Time hybrids: a new generic theory of reality Type Review
Year 2023 Publication Symmetry, Culture and Science Abbreviated Journal
Volume 34 Issue 3 Pages 347-351
Keywords Review; 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 ISBN Additional Links UA library record
Impact Factor (up) Times cited Open Access OpenAccess
Notes Approved Most recent IF: NA
Call Number UA @ admin @ c:irua:199538 Serial 8871
Permanent link to this record
 
 
Author Huang, L.; Ratkowsky, D.A.; Hui, C.; Gielis, J.; Lian, M.; Shi, P.
Title Inequality measure of leaf area distribution for a drought-tolerant landscape plant Type A1 Journal article
Year 2023 Publication Plants Abbreviated Journal
Volume 12 Issue 17 Pages 3143-11
Keywords A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
Abstract Measuring the inequality of leaf area distribution per plant (ILAD) can provide a useful tool for quantifying the influences of intra- and interspecific competition, foraging behavior of herbivores, and environmental stress on plants’ above-ground architectural structures and survival strategies. Despite its importance, there has been limited research on this issue. This paper aims to fill this gap by comparing four inequality indices to measure ILAD, using indices for quantifying household income that are commonly used in economics, including the Gini index (which is based on the Lorenz curve), the coefficient of variation, the Theil index, and the mean log deviation index. We measured the area of all leaves for 240 individual plants of the species Shibataea chinensis Nakai, a drought-tolerant landscape plant found in southern China. A three-parameter performance equation was fitted to observations of the cumulative proportion of leaf area vs. the cumulative proportion of leaves per plant to calculate the Gini index for each individual specimen of S. chinensis. The performance equation was demonstrated to be valid in describing the rotated and right shifted Lorenz curve, given that >96% of root-mean-square error values were smaller than 0.004 for 240 individual plants. By examining the correlation between any of the six possible pairs of indices among the Gini index, the coefficient of variation, the Theil index, and the mean log deviation index, the data show that these indices are closely related and can be used interchangeably to quantify ILAD.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Wos 001065193100001 Publication Date 2023-08-31
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 (up) Times cited Open Access OpenAccess
Notes Approved Most recent IF: NA
Call Number UA @ admin @ c:irua:199564 Serial 8886
Permanent link to this record
 
 
Author Shi, P.; Gielis, J.; Niklas, K.J.; Niinemets, Ü.; Schrader, J.
Title Leaf functional traits : ecological and evolutionary implications Type ME3 Book as editor
Year 2023 Publication Abbreviated Journal
Volume Issue Pages 185 p.
Keywords ME3 Book as editor; Sustainable Energy, Air and Water Technology (DuEL)
Abstract
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Wos Publication Date 2023-04-14
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN ISBN 978-2-8325-2086-4; 1664-8714 Additional Links UA library record
Impact Factor (up) Times cited Open Access OpenAccess
Notes Approved Most recent IF: NA
Call Number UA @ admin @ c:irua:198002 Serial 8894
Permanent link to this record
 
 
Author Gielis, J.
Title Simon Stevin as a central figure in the development of abstract algebra and generic programming Type A1 Journal article
Year 2023 Publication Symmetry : culture and science Abbreviated Journal
Volume 34 Issue 2 Pages 155-168
Keywords A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
Abstract Simon Stevin (1548-1620) is mainly known for the decimal system and his Clootkrans proof. His influence is also profound in infinitesimal calculus, mechanics, and even in abstract algebra and today’s conception of polynomials, algorithms, and generic programming. Here we review his influence as assessed in generic programming. According to Dr. Stepanov, one of the most influential researchers in generic programming, Stevin’s work on polynomials can be regarded as the essence of generic programming: an algorithm from one domain can be applied in another similar domain.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Wos 001068714100003 Publication Date 2023-07-11
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0865-4824 ISBN Additional Links UA library record; WoS full record
Impact Factor (up) Times cited Open Access Not_Open_Access: Available from 08.02.2024
Notes Approved Most recent IF: NA
Call Number UA @ admin @ c:irua:198000 Serial 8929
Permanent link to this record
 
 
Author Mescia, L.; Bia, P.; Gielis, J.; Caratelli, D.
Title Advanced particle swarm optimization methods for electromagnetics Type P1 Proceeding
Year 2023 Publication Abbreviated Journal
Volume Issue Pages 109-122 T2 - Proceedings of the 1st International
Keywords P1 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
Abstract Electromagnetic design problems involve optimizing multiple parameters that are nonlinearly related to objective functions. Traditional optimization techniques require significant computational resources that grow exponentially as the problem size increases. Therefore, a method that can produce good results with moderate memory and computational resources is desirable. Bioinspired optimization methods, such as particle swarm optimization (PSO), are known for their computational efficiency and are commonly used in various scientific and technological fields. In this article we explore the potential of advanced PSO-based algorithms to tackle challenging electromagnetic design and analysis problems faced in real-life applications. It provides a detailed comparison between conventional PSO and its quantum-inspired version regarding accuracy and computational costs. Additionally, theoretical insights on convergence issues and sensitivity analysis on parameters influencing the stochastic process are reported. The utilization of a novel quantum PSO-based algorithm in advanced scenarios, such as reconfigurable and shaped lens antenna synthesis, is illustrated. The hybrid modeling approach, based on the unified geometrical description enabled by the Gielis Transformation, is applied in combination with a suitable quantum PSO-based algorithm, along with a geometrical tube tracing and physical optics technique for solving the inverse problem aimed at identifying the geometrical parameters that yield optimal antenna performance.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Wos Publication Date 2023-11-29
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 978-90-833839-0-3 ISBN Additional Links UA library record
Impact Factor (up) Times cited Open Access
Notes Approved Most recent IF: NA
Call Number UA @ admin @ c:irua:201048 Serial 9002
Permanent link to this record
 
 
Author Gielis, J.
Title Conquering Mount Improbable Type P1 Proceeding
Year 2023 Publication Abbreviated Journal
Volume Issue Pages 153-173 T2 - Proceedings of the 1st International
Keywords P1 Proceeding; Economics; Sustainable Energy, Air and Water Technology (DuEL)
Abstract Our scientific and technological worldviews are largely dominated by the concepts of entropy and complexity. Originating in 19th-century thermodynamics, the concept of entropy merged with information in the last century, leading to definitions of entropy and complexity by Kolmogorov, Shannon and others. In its simplest form, this worldview is an application of the normal rules of arithmetic. In this worldview, when tossing a coin, a million heads or tails in a row is theoretically possible, but impossible in practice and in real life. On this basis, the impossible (in the binary case, the outermost entries of Pascal's triangle xn and yn for large values of n) can be safely neglected, and one can concentrate fully on what is common and what conforms to the law of large numbers, in fields ranging from physics to sociology and everything in between. However, in recent decades it has been shown that what is most improbable tends to be the rule in nature. Indeed, if one combines the outermost entries xn and yn with the normal rules of arithmetic, either addition or multiplication, one obtains Lamé curves and power laws respectively. In this article, some of these correspondences are highlighted, leading to a double conclusion. First, Gabriel Lamé's geometric footprint in mathematics and the sciences is enormous. Second, conic sections are at the core once more. Whereas mathematics so far has been exclusively the language of patterns in the sciences, the door is opened for mathematics to also become the language of the individual. The probabilistic worldview and Lamé's footprint can be seen as dual methods. In this context, it is to be expected that the notions of information, complexity, simplicity and redundancy benefit from this different viewpoint.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Wos Publication Date 2023-11-29
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 978-90-833839-0-3 ISBN Additional Links UA library record
Impact Factor (up) Times cited Open Access
Notes Approved Most recent IF: NA
Call Number UA @ admin @ c:irua:201045 Serial 9014
Permanent link to this record
 
 
Author Gielis, J.; Tavkhelidze, I.; Ricci, P.E.
Title Generalized Möbius-Listing bodies and the heart Type A3 Journal article
Year 2023 Publication Sn – 2247-689x Abbreviated Journal
Volume 13 Issue 2 Pages 58-70
Keywords A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
Abstract Generalized Möbius-Listing surfaces and bodies generalize Möbius bands, and this research was motivated originally by solutions of boundary value problems. Analogous to cutting of the original Möbius band, for this class of surfaces and bodies, results have been obtained when cutting such bodies or surfaces. The results can be applied in a wide range of fields in the natural science, and here we propose how they can serve as a model for the heart and the circulatory system.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Wos http://rjm-cs.ro/2023v13i2_7.pdf#page=1 Publication Date
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN ISBN Additional Links UA library record; http://rjm-cs.ro/2023v13i2_7.pdf#page=1
Impact Factor (up) Times cited Open Access
Notes Approved Most recent IF: NA
Call Number UA @ admin @ c:irua:200773 Serial 9043
Permanent link to this record
 
 
Author Gielis, J.; Tavkhelidze, I.
Title A note on Generalized Möbius-Listing Bodies Type P1 Proceeding
Year 2023 Publication Abbreviated Journal
Volume Issue Pages 31-39 T2 - Proceedings of the 1st International Sy
Keywords P1 Proceeding; Sustainable Energy, Air and Water Technology (DuEL)
Abstract Generalized Möbius-Listing surfaces and bodies generalize Möbius bands, and this research was motivated originally by solutions of boundary value problems. Analogous to cutting of the original Möbius band, for this class of surfaces and bodies, results have been obtained when cutting such bodies or surfaces. In general, cutting leads to interlinked and intertwined different surfaces or bodies, resulting in very complex systems. However, under certain conditions, the result of cutting can be a single surface or body, which reduces complexity considerably. These conditions are based on congruence and rotational symmetry of the resulting cross sections after cutting, and on the knife cutting the origin
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Wos Publication Date 2023-11-29
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 978-90-833839-0-3 ISBN Additional Links UA library record
Impact Factor (up) Times cited Open Access
Notes Approved Most recent IF: NA
Call Number UA @ admin @ c:irua:201047 Serial 9063
Permanent link to this record
 
 
Author Gao, J.; Huang, W.; Gielis, J.; Shi, P.
Title Plant morphology and function, geometric morphometrics, and modelling : decoding the mathematical secrets of plants Type Editorial
Year 2023 Publication Plants Abbreviated Journal
Volume 12 Issue 21 Pages 3724-2
Keywords Editorial; Sustainable Energy, Air and Water Technology (DuEL)
Abstract
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Wos 001103336500001 Publication Date 2023-10-30
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 2223-7747 ISBN Additional Links UA library record; WoS full record
Impact Factor (up) Times cited Open Access
Notes Approved Most recent IF: NA
Call Number UA @ admin @ c:irua:201173 Serial 9072
Permanent link to this record
 
 
Author Gao, J.; Huang, W.; Gielis, J.; Shi, P.
Title Plant morphology and function, geometric morphometrics, and modelling : decoding the mathematical secrets of plants Type ME3 Book as editor
Year 2023 Publication Abbreviated Journal
Volume Issue Pages 224 p.
Keywords ME3 Book as editor; Sustainable Energy, Air and Water Technology (DuEL)
Abstract Delve into the diverse aspects of plant morphology, their responses to global climate change, and the spatiotemporal dynamics of forest productivity. Join us on a journey through the intricate web of plant characteristics and their impact on the environment.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Wos Publication Date 2024-01-02
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN ISBN 978-3-0365-9422-4; 978-3-0365-9423-1 Additional Links UA library record
Impact Factor (up) Times cited Open Access
Notes Approved Most recent IF: NA
Call Number UA @ admin @ c:irua:201545 Serial 9073
Permanent link to this record
 
 
Author Gielis, J.; Brasili, S.
Title Proceedings of the 1st International Symposium on Square Bamboos and the Geometree (ISSBG 2022) Type ME3 Book as editor
Year 2023 Publication Abbreviated Journal
Volume Issue Pages xi, 175 p.
Keywords ME3 Book as editor; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
Abstract
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Wos Publication Date 2023-11-29
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN ISBN 978-90-833839-0-3 Additional Links UA library record
Impact Factor (up) Times cited Open Access
Notes Approved Most recent IF: NA
Call Number UA @ admin @ c:irua:201049 Serial 9077
Permanent link to this record
 
 
Author Li, Y.; Quinn, B.K.; Niinemets, Ü.; Schrader, J.; Gielis, J.; Liu, M.; Shi, P.
Title Ellipticalness index : a simple measure of the complexity of oval leaf shape Type A1 Journal article
Year 2022 Publication Pakistan journal of botany : An official publication of pakistan botanical society Abbreviated Journal Pak J Bot
Volume 54 Issue 6 Pages 1-8
Keywords A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
Abstract Plants have diverse leaf shapes that have evolved to adapt to the environments they have experienced over their evolutionary history. Leaf shape and leaf size can greatly influence the growth rate, competitive ability, and productivity of plants. However, researchers have long struggled to decide how to properly quantify the complexity of leaf shape. Prior studies recommended the leaf roundness index (RI = 4πA/P2) or dissection index (DI = ), where P is leaf perimeter and A is leaf area. However, these two indices merely measure the extent of the deviation of leaf shape from a circle, which is usually invalid as leaves are seldom circular. In this study, we proposed a simple measure, named the ellipticalness index (EI), for quantifying the complexity of leaf shape based on the hypothesis that the shape of any oval leaf can be regarded as a variation from a standard ellipse. 2220 leaves from nine species of Magnoliaceae were sampled to check the validity of the EI. We also tested the validity of the Montgomery equation (ME), which assumes a proportional relationship between leaf area and the product of leaf length and width, because the EI actually comes from the proportionality coefficient of the ME. We also compared the ME with five other models of leaf area. The ME was found to be the best model for calculating leaf area based on consideration of the trade-off between model fit vs. complexity, which strongly supported the robustness of the EI for describing oval leaf shape. The new index can account for both leaf shape and size, and we conclude that it is a promising method for quantifying and comparing oval leaf shapes across species in future studies.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Wos 000814279700028 Publication Date 2022-05-23
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0556-3321 ISBN Additional Links UA library record; WoS full record; WoS citing articles
Impact Factor (up) 1.2 Times cited Open Access OpenAccess
Notes Approved Most recent IF: 1.2
Call Number UA @ admin @ c:irua:188469 Serial 7153
Permanent link to this record
 
 
Author Wang, L.; Shi, P.; Chen, L.; Gielis, J.; Niklas, K.J.
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 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 (up) 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
Permanent link to this record
 
 
Author Li, Q.; Niklas, K.J.J.; Niinemets, U.; Zhang, L.; Yu, K.; Gielis, J.; Gao, J.; Shi, P.
Title Stomatal shape described by a superellipse in four Magnoliaceae species Type A1 Journal article
Year 2023 Publication Botany letters Abbreviated Journal
Volume Issue Pages 1-9
Keywords A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
Abstract Stomata are essential for the exchange of water vapour and atmospheric gases between vascular plants and their external environments. The stomatal geometries of many plants appear to be elliptical. However, prior studies have not tested whether this is a mathematical reality, particularly since many natural shapes that appear to be ellipses are superellipses with greater or smaller edge curvature than predicted for an ellipse. Compared with the ellipse equation, the superellipse equation includes an additional parameter that allows generation of a larger range of shapes. We randomly selected 240 stomata from each of four Magnoliaceae species to test whether the stomatal geometries are superellipses or ellipses. The stomatal geometries for most stomata (943/960) were found to be described better using the superellipse equation. The traditional “elliptical stomata hypothesis” resulted in an underestimation of the area of stomata, whereas the superellipse equation accurately predicted stomatal area. This finding has important implications for the estimation of stomatal area in studies looking at stomatal shape, geometry, and function.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Wos 001024190300001 Publication Date 2023-07-12
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 (up) 1.5 Times cited Open Access Not_Open_Access: Available from 12.01.2024
Notes Approved Most recent IF: 1.5; 2023 IF: NA
Call Number UA @ admin @ c:irua:197847 Serial 8935
Permanent link to this record
 
 
Author Yao, W.; Hui, C.; Wang, L.; Wang, J.; Gielis, J.; Shi, P.
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 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 (up) 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
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Author Shi, P.; Yu, K.; Niinemets, Ü.; Gielis, J.
Title Can leaf shape be represented by the ratio of leaf width to length? Evidence from nine species of Magnolia and Michelia (Magnoliaceae) Type A1 Journal article
Year 2021 Publication Forests Abbreviated Journal Forests
Volume 12 Issue 1 Pages 41
Keywords A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
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.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Wos 000611074700001 Publication Date 2020-12-31
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 (up) 1.951 Times cited Open Access OpenAccess
Notes Approved Most recent IF: 1.951
Call Number UA @ admin @ c:irua:174473 Serial 7572
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Author Lian, M.; Shi, P.; Zhang, L.; Yao, W.; Gielis, J.; Niklas, K.J.
Title A generalized performance equation and its application in measuring the Gini index of leaf size inequality Type A1 Journal article
Year 2023 Publication Trees: structure and function Abbreviated Journal
Volume 37 Issue Pages 1555-1565
Keywords A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
Abstract The goal of this study is to provide a rigorous tool to quantify the inequality of the leaf size distribution of an individual plant, thereby serving as a reference trait for quantifying plant adaptations to local environmental conditions. The tool to be presented and tested employs three components: (1) a performance equation (PE), which can produce flexible asymmetrical and symmetrical bell-shaped curves, (2) the Lorenz curve (i.e., the cumulative proportion of leaf size vs. the cumulative proportion of number of leaves), which is the basis for calculating, and (3) the Gini index, which measures the inequality of leaf size distribution. We sampled 12 individual plants of a dwarf bamboo and measured the area and dry mass of each leaf of each plant. We then developed a generalized performance equation (GPE) of which the PE is a special case and fitted the Lorenz curve to leaf size distribution using the GPE and PE. The GPE performed better than the PE in fitting the Lorenz curve. We compared the Gini index of leaf area distribution with that of leaf dry mass distribution and found that there was a significant difference between the two indices that might emerge from the scaling relationship between leaf dry mass and area. Nevertheless, there was a strong correlation between the two Gini indices (r2 = 0.9846). This study provides a promising tool based on the GPE for quantifying the inequality of leaf size distributions across individual plants and can be used to quantify plant adaptations to local environmental conditions.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Wos 001069570200001 Publication Date 2023-08-26
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0931-1890; 1432-2285 ISBN Additional Links UA library record; WoS full record; WoS citing articles
Impact Factor (up) 2.3 Times cited Open Access Not_Open_Access: Available from 26.02.2024
Notes Approved Most recent IF: 2.3; 2023 IF: 1.842
Call Number UA @ admin @ c:irua:199562 Serial 8874
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Author Shi, P.; Ratkowsky, D.A.; Gielis, J.
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 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 (up) 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 Li, Y.; Quinn, B.K.; Gielis, J.; Li, Y.; Shi, P.
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 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 (up) 2.7 Times cited Open Access OpenAccess
Notes Approved Most recent IF: 2.7
Call Number UA @ admin @ c:irua:186453 Serial 7158
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Author Shi, P.; Wang, L.; Quinn, B.K.K.; Gielis, J.
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 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 (up) 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
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Author Wang, L.; Ratkowsky, D.A.; Gielis, J.; Ricci, P.E.; Shi, P.
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 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 (up) 2.7 Times cited Open Access OpenAccess
Notes Approved Most recent IF: 2.7
Call Number UA @ admin @ c:irua:191860 Serial 7301
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Author Huang, W.; Li, Y.; Niklas, K.J.; Gielis, J.; Ding, Y.; Cao, L.; Shi, P.
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 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 (up) 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