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Gielis, J.; Caratelli, D.; Shi, P.; Ricci, P.E. |
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Title |
A note on spirals and curvature |
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A1 Journal article |
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Year |
2020 |
Publication |
Growth and form |
Abbreviated Journal |
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Volume |
1 |
Issue |
1 |
Pages |
1-8 |
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Keywords |
A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
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Abstract |
Starting from logarithmic, sinusoidal and power spirals, it is shown how these spirals are connected directly with Chebyshev polynomials, Lamé curves, with allometry and Antonelli-metrics in Finsler geometry. Curvature is a crucial concept in geometry both for closed curves and equiangular spirals, and allowed Dillen to give a general definition of spirals. Many natural shapes can be described as a combination of one of two basic shapes in nature—circle and spiral—with Gielis transformations. Using this idea, shape description itself is used to develop a novel approach to anisotropic curvature in nature. Various examples are discussed, including fusion in flowers and its connection to the recently described pseudo-Chebyshev functions. |
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2020-02-23 |
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Most recent IF: NA |
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Call Number |
UA @ admin @ c:irua:167061 |
Serial |
6569 |
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Author |
De Tommasi, E.; Rogato, A.; Caratelli, D.; Mescia, L.; Gielis, J. |
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Title |
Following the photons route : mathematical models describing the interaction of diatoms with light |
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H1 Book chapter |
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Year |
2022 |
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1-53 |
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Keywords |
H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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Abstract |
The interaction of diatoms with sunlight is fundamental in order to deeply understand their role in terrestrial ecology and biogeochemistry, essentially due to their massive contribution to global primary production through photosynthesis and its e↵ect on carbon, oxygen and silicon cycles. Following the journey of light through natural waters, its propagation through the intricate frustule micro- and nano-structure and, finally, its fate inside the photosynthetic machinery of the living cell requires several mathematical and computational models in order to accurately describe all the involved phenomena taking place at di↵erent space scales and physical regimes. In this chapter, we review the main analytical models describing the underwater optical field, the essential numerical algorithms for the study of photonic properties of the diatom frustule seen as a natural metamaterial, as well as the principal models describing photon harvesting in diatom plastids and methods for complex EM propagation problems and wave propagation in dispersive materials with multiple relaxation times. These mathematical methods will be integrated in a unifying geometric perspective. |
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ISBN |
978-1-119-74985-1 |
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Most recent IF: NA |
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Call Number |
UA @ admin @ c:irua:186731 |
Serial |
7165 |
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Author |
Gielis, J.; Shi, P.; Caratelli, D. |
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Title |
Universal equations : a fresh perspective |
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A1 Journal article |
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Year |
2022 |
Publication |
Growth and Form |
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Keywords |
A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
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Abstract |
A uniform description of natural shapes and phenomena is an important goal in science. Such description should check some basic principles, related to 1) the complexity of the model, 2) how well its fits real objects, phenomena and data, and 3) ia direct connection with optimization principles and the calculus of variations. In this article, we present nine principles, three for each group, and we compare some models with a claim to universality. It is also shown that Gielis Transformations and power laws have a common origin in conic sections |
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Most recent IF: NA |
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Call Number |
UA @ admin @ c:irua:189317 |
Serial |
7224 |
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Author |
Gielis, J.; Caratelli, D.; Fougerolle, Y.; Ricci, P.E.; Gerats, T. |
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Title |
A biogeometrical model for corolla fusion in Asclepiad flowers |
Type |
H1 Book chapter |
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Year |
2017 |
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Abbreviated Journal |
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Volume |
2 |
Issue |
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Pages |
83-105
T2 - Modeling in mathematics : proceedings |
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Keywords |
H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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Abstract |
The molecular genetics of flower development have been studied extensively for more than two decades. Fusion of organs and the tendency to oligomery, important characteristics of flower evolution, so far have remained fairly elusive. We present a geometric model for shape and fusion in the corolla of Asclepiads. Examples demonstrate how fusion of petals creates stable centers, a prerequisite for the formation of complex pollination structures via congenital and postgenital fusion events, with the formation of de novo organs, specific to Asclepiads. The development of the corolla reduces to simple inequalities from the MATHS-BOX. The formation of stable centers and of bell and tubular shapes in flowers are immediate and logical consequences of the shape. Our model shows that any study on flowers, especially in evo-devo perspective should be performed within the wider framework of polymery and oligomery and of fusion and synorganization. |
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000442076400007 |
Publication Date |
2017-04-20 |
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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 |
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no |
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Call Number |
UA @ admin @ c:irua:144551 |
Serial |
7561 |
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Author |
Gielis, J.; Caratelli, D.; Tavkelidze, I.; Fougerolle, Y.; Ricci, P.E.; Gerats, T. |
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Title |
Bulky knots and links generated by cutting generalized Mobius-Listing bodies and applications in the natural sciences |
Type |
H2 Book chapter |
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Year |
2013 |
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Pages |
167-183
T2 - Math Art Summit : Koninklijke Vlaamse |
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Keywords |
H2 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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978-90-6569-119-4 |
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no |
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Call Number |
UA @ admin @ c:irua:110955 |
Serial |
7569 |
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Author |
Gielis, J.; Caratelli, D.; de Jong van Coevorden, M.; Ricci, P.E. |
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Title |
The common descent of biological shape description and special functions |
Type |
H1 Book chapter |
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Year |
2018 |
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230 |
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Pages |
119-131
T2 - Differential and difference equations |
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Keywords |
H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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Abstract |
Gielis transformations, with their origin in botany, are used to define square waves and trigonometric functions of higher order. They are rewritten in terms of Chebyshev polynomials. The origin of both, a uniform descriptor and the origin of orthogonal polynomials, can be traced back to a letter of Guido Grandi to Leibniz in 1713 on the mathematical description of the shape of flowers. In this way geometrical description and analytical tools are seamlessly combined. |
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000451375900010 |
Publication Date |
2018-05-08 |
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978-3-319-75646-2; 2194-1009; 978-3-319-75647-9; 978-3-319-75646-2 |
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UA library record; WoS full record; WoS citing articles |
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no |
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Call Number |
UA @ admin @ c:irua:150949 |
Serial |
7685 |
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Author |
Bia, P.; Caratelli, D.; Mescia, L.; Gielis, J. |
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Title |
Electromagnetic characterization of supershaped lens antennas for high-frequency applications |
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H1 Book chapter |
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Year |
2013 |
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Pages |
1679-1682
T2 - Proceedings of the 43rd European Mi |
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Keywords |
H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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000330768700424 |
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978-2-87487-031-6 |
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UA library record; WoS full record; WoS citing articles |
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no |
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Call Number |
UA @ admin @ c:irua:110954 |
Serial |
7865 |
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Author |
Caratelli, D.; Gielis, J.; Ricci, P.E. |
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Title |
Fourier-like solution of the Dirichlet problem for the Laplace Equation in k-type Gielis domains |
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A1 Journal article |
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Year |
2011 |
Publication |
Journal of pure and applied mathematics : advances and applications |
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5 |
Issue |
2 |
Pages |
99-111 |
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Keywords |
A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
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Abstract |
The interior and exterior Dirichlet problems for the Laplace equation in k-type Gielis domains are analytically addressed by using a suitable Fourier-like technique. A dedicated numerical procedure based on the computer-aided algebra tool 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. Computed results are found to be in good agreement with theoretical findings on Fourier series expansion presented by Carleson. |
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no |
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Call Number |
UA @ admin @ c:irua:91090 |
Serial |
7982 |
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Author |
Gielis, J.; Caratelli, D.; Tavkhelidze, I. |
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Title |
The general case of cutting GML bodies : the geometrical solution |
Type |
H1 Book chapter |
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Year |
2020 |
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Pages |
397-411
T2 - Differential and difference equations |
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Keywords |
H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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2020-10-21 |
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978-3-030-56322-6 |
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Most recent IF: NA |
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Call Number |
UA @ admin @ c:irua:174477 |
Serial |
7991 |
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Author |
Gielis, J.; Shi, P.; Beirinckx, B.; Caratelli, D.; Ricci, P.E. |
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Title |
Lamé-Gielis curves in biology and geometry |
Type |
P3 Proceeding |
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Year |
2021 |
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P3 Proceeding; Sustainable Energy, Air and Water Technology (DuEL) |
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Most recent IF: NA |
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Call Number |
UA @ admin @ c:irua:178828 |
Serial |
8145 |
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Author |
Tavkhelidze, I.; Caratelli, D.; Gielis, J.; Ricci, P.E.; Rogava, M.; Transirico, M. |
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Title |
On a geometric model of bodies with “complex” configuration and some movements |
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2017 |
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2 |
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Pages |
129-158
T2 - Modeling in mathematics : proceedings |
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Keywords |
H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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Abstract |
Aim of this chapter is analytical representation of one wide class of geometric figures (lines, surfaces and bodies) and their complicated displacements. The accurate estimation of physical characteristics (such as volume, surface area, length, or other specific parameters) relevant to human organs is of fundamental importance in medicine. One central idea of this article is, in this respect, to provide a general methodology for the evaluation, as a function of time, of the volume and center of gravity featured by moving of one class of bodies used of describe different human organs. |
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000442076400010 |
Publication Date |
2017-04-20 |
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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 |
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no |
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Call Number |
UA @ admin @ c:irua:144552 |
Serial |
8326 |
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Author |
Caratelli, D.; Gielis, J.; Ricci, P.E.; Tavkhelidze, I. |
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Title |
Some properties of “bulky” links, generated by Generalized Möbius Listing's bodies GML4n |
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P3 Proceeding |
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2013 |
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P3 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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Call Number |
UA @ admin @ c:irua:108672 |
Serial |
8555 |
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