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	Author	Caratelli, D.; Gielis, J.; Tavkhelidze, I.; Ricci, P.E.
	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	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	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		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:107177			Serial	8576
Permanent link to this record



	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
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000695118600001	Publication Date	2021-09-12
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1007-662x; 1993-0607	ISBN		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



	Author	Lin, S.; Zhang, L.; Reddy, G.V.P.; Hui, C.; Gielis, J.; Ding, Y.; Shi, P.
	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	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	Huang, W.; Su, X.; Ratkowsky, D.A.; Niklas, K.J.; Gielis, J.; Shi, P.
	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	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	Chapman, D.; Gielis, J.
	Title	Gielis transformations for the audiovisual geometry database			Type	A1 Journal article
	Year	2021	Publication	Symmetry : culture and science	Abbreviated Journal
	Volume	32	Issue	2	Pages	177-180
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	This publication introduces the audiovisual geometry database with Gielis transformations as initial records for a prototype of the database. A concise overview is given of the rationale behind the database and studying wave phenomena with Gielis transformations. First results on a form of timbral polyphony observed in Gielis curves and future work are briefly discussed.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		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
	Impact Factor		Times cited		Open Access	Not_Open_Access
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:180965			Serial	8004
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.
	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	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	Gielis, J.; Natalini, P.; Ricci, P.E.
	Title	A note about generalized forms of the Gielis formula			Type	H1 Book chapter
	Year	2017	Publication		Abbreviated Journal
	Volume	2	Issue		Pages	107-116 T2 - Modeling in mathematics : proceedings
	Keywords	H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	We generalize the Gielis Superformula by extending the R. Chacon approach, but avoiding the use of Jacobi elliptic functions. The obtained results are extended to the three-dimensional case. Several new shapes are derived by using the computer algebra system Mathematica(C).
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000442076400008	Publication Date	2017-04-20
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		ISBN	978-94-6239-260-1; 978-94-6239-261-8; 2543-0300; 978-94-6239-260-1	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:144550			Serial	8318
Permanent link to this record