| Records |
| Author |
Li, Y.; Niklas, K.J.; Gielis, J.; Niinemets, Ü.; Schrader, J.; Wang, R.; Shi, P. |
| Title |
An elliptical blade is not a true ellipse, but a superellipse : evidence from two Michelia species |
Type |
A1 Journal article |
| Year |
2022 |
Publication |
Journal of forestry research |
Abbreviated Journal  |
J Forestry Res |
| Volume |
33 |
Issue |
4 |
Pages |
1341-1348 |
| Keywords |
A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
The shape of leaf laminae exhibits considerable diversity and complexity that reflects adaptations to environmental factors such as ambient light and precipitation as well as phyletic legacy. Many leaves appear to be elliptical which may represent a ‘default’ developmental condition. However, whether their geometry truly conforms to the ellipse equation (EE), i.e., (x/a)2 + (y/b)2 = 1, remains conjectural. One alternative is described by the superellipse equation (SE), a generalized version of EE, i.e., |x/a|n +|y/b|n = 1. To test the efficacy of EE versus SE to describe leaf geometry, the leaf shapes of two Michelia species (i.e., M. cavaleriei var. platypetala, and M. maudiae), were investigated using 60 leaves from each species. Analysis shows that the majority of leaves (118 out of 120) had adjusted root-mean-square errors of < 0.05 for the nonlinear fitting of SE to leaf geometry, i.e., the mean absolute deviation from the polar point to leaf marginal points was smaller than 5% of the radius of a hypothesized circle with its area equaling leaf area. The estimates of n for the two species were ˂ 2, indicating that all sampled leaves conformed to SE and not to EE. This study confirms the existence of SE in leaves, linking this to its potential functional advantages, particularly the possible influence of leaf shape on hydraulic conductance. |
| Address |
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| Corporate Author |
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Thesis |
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| Publisher |
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Place of Publication |
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Editor |
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| Language |
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Wos |
000695118600001 |
Publication Date |
2021-09-12 |
| Series Editor |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
|
Series Issue |
|
Edition |
|
| ISSN |
1007-662x; 1993-0607 |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
| Impact Factor |
3 |
Times cited |
|
Open Access |
OpenAccess |
| Notes |
|
Approved |
Most recent IF: 3 |
| Call Number |
UA @ admin @ c:irua:180967 |
Serial |
7152 |
| Permanent link to this record |
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| |
| 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 |
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| Corporate Author |
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Thesis |
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| Publisher |
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Place of Publication |
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Editor |
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| Language |
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Wos |
000814279700028 |
Publication Date |
2022-05-23 |
| Series Editor |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
|
Edition |
|
| ISSN |
0556-3321 |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
| Impact Factor |
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 |
| |
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| |
| Author |
Gielis, J. |
| Title |
Double helix of phyllotaxis : analysis of the geometric model of plant morphogenesis, by Boris Rozin |
Type |
Review |
| Year |
2021 |
Publication |
Quarterly Review Of Biology |
Abbreviated Journal |
Q Rev Biol |
| Volume |
96 |
Issue |
2 |
Pages |
139-140 |
| Keywords |
Review; Sustainable Energy, Air and Water Technology (DuEL) |
| Abstract |
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| Address |
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| Corporate Author |
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Thesis |
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| Publisher |
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Place of Publication |
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Editor |
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| Language |
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Wos |
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Publication Date |
2021-05-19 |
| Series Editor |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
|
Edition |
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| ISSN |
0033-5770; 1539-7718 |
ISBN |
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Additional Links |
UA library record |
| Impact Factor |
4.25 |
Times cited |
|
Open Access |
Not_Open_Access |
| Notes |
|
Approved |
Most recent IF: 4.25 |
| Call Number |
UA @ admin @ c:irua:178829 |
Serial |
7824 |
| Permanent link to this record |
| |
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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 |
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| Corporate Author |
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Thesis |
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| Publisher |
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Place of Publication |
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Editor |
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| Language |
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Wos |
000540222200156 |
Publication Date |
2020-04-21 |
| Series Editor |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
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Edition |
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| ISSN |
2073-8994 |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
| Impact Factor |
2.7 |
Times cited |
4 |
Open Access |
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| 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 |
| Permanent link to this record |
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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 |
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| Corporate Author |
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Thesis |
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| Publisher |
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Place of Publication |
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Editor |
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| Language |
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Wos |
000746030100001 |
Publication Date |
2021-12-27 |
| Series Editor |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
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Edition |
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| ISSN |
2073-8994 |
ISBN |
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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 |
| |
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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 |
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| Corporate Author |
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Thesis |
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| Publisher |
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Place of Publication |
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Editor |
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| Language |
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Wos |
000927531000001 |
Publication Date |
2023-01-13 |
| Series Editor |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
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Edition |
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| ISSN |
2073-8994 |
ISBN |
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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 |
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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 |
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| Corporate Author |
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Thesis |
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| Publisher |
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Place of Publication |
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Editor |
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| Language |
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Wos |
000904525700001 |
Publication Date |
2022-11-23 |
| Series Editor |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
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Edition |
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| ISSN |
2073-8994 |
ISBN |
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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 |
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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 |
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| Corporate Author |
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Thesis |
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| Publisher |
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Place of Publication |
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Editor |
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| Language |
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Wos |
000602546300001 |
Publication Date |
2020-12-15 |
| Series Editor |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
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Edition |
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| 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 |
