|
“About “bulky&rdquo, links generated by generalized Möbius-Listing bodies GML2n”. Gielis J, Tavkhelidze I, Ricci PE, Journal of mathematical sciences 193, 449 (2013). http://doi.org/10.1007/S10958-013-1474-7
Abstract: In this paper, we consider the bulky knots and bulky links, which appear after cutting of a Generalized MöbiusListing GMLn2 body (with the radial cross section a convex plane 2-symmetric figure with two vertices) along a different Generalized MöbiusListing surfaces GMLn2 situated in it. The aim of this report is to investigate the number and geometric structure of the independent objects that appear after such a cutting process of GMLn2 bodies. In most cases we are able to count the indices of the resulting mathematical objects according to the known classification for the standard knots and links.
Keywords: A2 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1007/S10958-013-1474-7
|
|
|
“Modeling of electroporation induced by pulsed electric fields in irregularly shaped cells”. Mescia L, Chiapperino MA, Bia P, Gielis J, Caratelli D, IEEE transactions on biomedical engineering 65, 414 (2018). http://doi.org/10.1109/TBME.2017.2771943
Abstract: During the past decades, the poration of cell membrane induced by pulsed electric fields has been widely investigated. Since the basic mechanisms of this process have not yet been fully clarified, many research activities are focused on the development of suitable theoretical and numerical models. To this end, a nonlinear, nonlocal, dispersive, and space-time numerical algorithm has been developed and adopted to evaluate the transmembrane voltage and pore density along the perimeter of realistic irregularly shaped cells. The presented model is based on the Maxwell's equations and the asymptotic Smoluchowski's equation describing the pore dynamics. The dielectric dispersion of the media forming the cell has been modeled by using a general multirelaxation Debye-based formulation. The irregular shape of the cell is described by using the Gielis' superformula. Different test cases pertaining to red blood cells, muscular cells, cell in mitosis phase, and cancer-like cell have been investigated. For each type of cell, the influence of the relevant shape, the dielectric properties, and the external electric pulse characteristics on the electroporation process has been analyzed. The numerical results demonstrate that the proposed model is an efficient numerical tool to study the electroporation problem in arbitrary-shaped cells.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1109/TBME.2017.2771943
|
|
|
“The general case of cutting GML bodies : the geometrical solution”. Gielis J, Caratelli D, Tavkhelidze I page 397 (2020).
Keywords: H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1007/978-3-030-56323-3_31
|
|
|
“About some methods of analytic representation and classification of a wide set of geometric figures with “complex” configuration”. Tavkhelidze I, Gielis J, Pinelas S page 347 (2020).
Keywords: H1 Book chapter; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1007/978-3-030-56323-3_27
|
|
|
Gielis J (2023) Fred Van Oystaeyen : Time hybrids: a new generic theory of reality. 347–351
Keywords: Review; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.26830/SYMMETRY_2023_3_357
|
|
|
“Nonlinear dispersive model of electroporation for irregular nucleated cells”. Chiapperino MA, Bia P, Caratelli D, Gielis J, Mescia L, Dermol-Cerne J, Miklavcic D, Bioelectromagnetics 40, 331 (2019). http://doi.org/10.1002/BEM.22197
Abstract: In this work, the electroporation phenomenon induced by pulsed electric field on different nucleated biological cells is studied. A nonlinear, non-local, dispersive, and space-time multiphysics model based on Maxwell's and asymptotic Smoluchowski's equations has been developed to calculate the transmembrane voltage and pore density on both plasma and nuclear membrane perimeters. The irregular cell shape has been modeled by incorporating in the numerical algorithm the analytical functions pertaining to Gielis curves. The dielectric dispersion of the cell media has been modeled considering the multi-relaxation Debye-based relationship. Two different irregular nucleated cells have been investigated and their response has been studied applying both the dispersive and non-dispersive models. By a comparison of the obtained results, differences can be highlighted confirming the need to make use of the dispersive model to effectively investigate the cell response in terms of transmembrane voltages, pore densities, and electroporation opening angle, especially when irregular cell shapes and short electric pulses are considered. Bioelectromagnetics. 2019;40:331-342. (c) 2019 Wiley Periodicals, Inc.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1002/BEM.22197
|
|
|
“Spherical harmonic solution of the Robin problem for the Helmholtz equation in a supershaped shell”. Caratelli D, Gielis J, Tavkhelidze I, Ricci PE, Applied mathematics 4, 263 (2013). http://doi.org/10.4236/AM.2013.41A040
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.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.4236/AM.2013.41A040
|
|
|
“Fourier-Hankel solution of the Robin problem for the Helmholtz equation in supershaped annular domains”. Caratelli D, Gielis J, Tavkhelidze I, Ricci PE, Boundary value problems , 253 (2013). http://doi.org/10.1186/1687-2770-2013-253
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.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1186/1687-2770-2013-253
|
|
|
“A new program to estimate the parameters of Preston's equation, a general formula for describing the egg shape of birds”. Shi P, Wang L, Quinn BKK, Gielis J, Symmetry 15, 231 (2023). http://doi.org/10.3390/SYM15010231
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.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
Impact Factor: 2.7
DOI: 10.3390/SYM15010231
|
|
|
Gielis J (2017) The geometrical beauty of plants. 229 p
Keywords: MA3 Book as author; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.2991/978-94-6239-151-2
|
|
|
“Plant morphology and function, geometric morphometrics, and modelling : decoding the mathematical secrets of plants”. Gao J, Huang W, Gielis J, Shi P page 224 p. (2023).
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.
Keywords: ME3 Book as editor; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.3390/BOOKS978-3-0365-9423-1
|
|
|
“Modeling in mathematics : proceedings of the second Tbilisi-Salerno workshop on modeling in mathematics”. Gielis J, Ricci PE, Tavkhelidze I page 185 p. (2017).
Keywords: ME3 Book as editor; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.2991/978-94-6239-261-8
|
|
|
“Leaf functional traits : ecological and evolutionary implications”. Shi P, Gielis J, Niklas KJ, Niinemets Ü, Schrader J page 185 p. (2023).
Keywords: ME3 Book as editor; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.3389/978-2-83252-086-4
|
|
|
“Proportional relationship between leaf area and the product of leaf length and width of four types of special leaf shapes”. Shi P, Liu M, Yu X, Gielis J, Ratkowsky DA, Forests (19994907) 10, 178 (2019). http://doi.org/10.3390/F10020178
Abstract: The leaf area, as an important leaf functional trait, is thought to be related to leaf length and width. Our recent study showed that the Montgomery equation, which assumes that leaf area is proportional to the product of leaf length and width, applied to different leaf shapes, and the coefficient of proportionality (namely the Montgomery parameter) range from 1/2 to π/4. However, no relevant geometrical evidence has previously been provided to support the above findings. Here, four types of representative leaf shapes (the elliptical, sectorial, linear, and triangular shapes) were studied. We derived the range of the estimate of the Montgomery parameter for every type. For the elliptical and triangular leaf shapes, the estimates are π/4 and 1/2, respectively; for the linear leaf shape, especially for the plants of Poaceae that can be described by the simplified Gielis equation, the estimate ranges from 0.6795 to π/4; for the sectorial leaf shape, the estimate ranges from 1/2 to π/4. The estimates based on the observations of actual leaves support the above theoretical results. The results obtained here show that the coefficient of proportionality of leaf area versus the product of leaf length and width only varies in a small range, maintaining the allometric relationship for leaf area and thereby suggesting that the proportional relationship between leaf area and the product of leaf length and width broadly remains stable during leaf evolution.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.3390/F10020178
|
|
|
“Gielis transformations for the audiovisual geometry database”. Chapman D, Gielis J, Symmetry : culture and science 32, 177 (2021). http://doi.org/10.26830/SYMMETRY_2021_2_177
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.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.26830/SYMMETRY_2021_2_177
|
|
|
“Proceedings of the 1st International Symposium on Square Bamboos and the Geometree (ISSBG 2022)”. Gielis J, Brasili S page xi, 175 p. (2023).
Keywords: ME3 Book as editor; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.55060/s.atmps.231115.000
|
|
|
“Design of irregularly shaped lens antennas including supershaped feed”. Mescia L, Lamacchia CM, Chiapperino MA, Bia P, Gielis J, Caratelli D, Progress in Electromagnetic Research Symposium (PIERS)
T2 –, 2019 PhotonIcs &, Electromagnetics Research Symposium –, Spring (PIERS-Spring), 17-20 June, 2019, Rome, Italy , 169 (2019). http://doi.org/10.1109/PIERS-SPRING46901.2019.9017900
Abstract: A new class of irregularly shaped dielectric lens antennas with a supershaped microstrip antenna feeder is presented and detailed in this work. The surface of the lens antenna and the feeder shape have been modelled by using the three and two-dimensional Gielis formula, respectively. The antenna design has been carried out by integrating an home-made software tool with the CST Microwave Studio®. The radiation properties of the whole antenna system have been evaluated using a dedicated high-frequency technique based on the tube tracing approximation. Moreover, the effects due to the multiple internal reflections have been properly modeled. The proposed model was applied to study unusual and complex lens antenna systems with the aim to design special radiation characteristics.
Keywords: P1 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1109/PIERS-SPRING46901.2019.9017900
|
|
|
“Bulky knots and links generated by cutting generalized Mobius-Listing bodies and applications in the natural sciences”. Gielis J, Caratelli D, Tavkelidze I, Fougerolle Y, Ricci PE, Gerats T page 167 (2013).
Keywords: H2 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
|
|
|
“The apeirogon and dual numbers”. Gielis J, Brasili S, Symmetry : culture and science 32, 157 (2021). http://doi.org/10.26830/SYMMETRY_2021_2_157
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.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.26830/SYMMETRY_2021_2_157
|
|
|
“Simon Stevin as a central figure in the development of abstract algebra and generic programming”. Gielis J, Symmetry : culture and science 34, 155 (2023). http://doi.org/10.26830/SYMMETRY_2023_2_155
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.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.26830/SYMMETRY_2023_2_155
|
|
|
“Conquering Mount Improbable”. Gielis J, , 153 (2023). http://doi.org/10.55060/s.atmps.231115.013
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.
Keywords: P1 Proceeding; Economics; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.55060/s.atmps.231115.013
|
|
|
Ricci PE, Gielis J (2022) From Pythagoras to Fourier and from geometry to nature. 146 p
Keywords: MA3 Book as author; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.55060/B.P2FG2N.220215.000
|
|
|
Gielis J (2021) Double helix of phyllotaxis : analysis of the geometric model of plant morphogenesis, by Boris Rozin. 139–140
Keywords: Review; Sustainable Energy, Air and Water Technology (DuEL)
Impact Factor: 4.25
DOI: 10.1086/714470
|
|
|
“On a geometric model of bodies with “complex” configuration and some movements”. Tavkhelidze I, Caratelli D, Gielis J, Ricci PE, Rogava M, Transirico M page 129 (2017).
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.
Keywords: H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.2991/978-94-6239-261-8_10
|
|
|
“‘biogeom&rsquo, : an R package for simulating and fitting natural shapes”. Shi P, Gielis J, Quinn BK, Niklas KJ, Ratkowsky DA, Schrader J, Ruan H, Wang L, Niinemets Ü, Niinennets U, Annals of the New York Academy of Sciences 1516, 123 (2022). http://doi.org/10.1111/NYAS.14862
Abstract: Many natural objects exhibit radial or axial symmetry in a single plane. However, a universal tool for simulating and fitting the shapes of such objects is lacking. Herein, we present an R package called 'biogeom' that simulates and fits many shapes found in nature. The package incorporates novel universal parametric equations that generate the profiles of bird eggs, flowers, linear and lanceolate leaves, seeds, starfish, and tree-rings, and three growth-rate equations that generate the profiles of ovate leaves and the ontogenetic growth curves of animals and plants. 'biogeom' includes several empirical datasets comprising the boundary coordinates of bird eggs, fruits, lanceolate and ovate leaves, tree rings, seeds, and sea stars. The package can also be applied to other kinds of natural shapes similar to those in the datasets. In addition, the package includes sigmoid curves derived from the three growth-rate equations, which can be used to model animal and plant growth trajectories and predict the times associated with maximum growth rate. 'biogeom' can quantify the intra- or interspecific similarity of natural outlines, and it provides quantitative information of shape and ontogenetic modification of shape with important ecological and evolutionary implications for the growth and form of the living world.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
Impact Factor: 5.2
DOI: 10.1111/NYAS.14862
|
|
|
“The common descent of biological shape description and special functions”. Gielis J, Caratelli D, de Jong van Coevorden M, Ricci PE page 119 (2018).
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.
Keywords: H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1007/978-3-319-75647-9_10
|
|
|
“A simple way to calculate the volume and surface area of avian eggs”. Shi P, Chen L, Quinn BK, Yu K, Miao Q, Guo X, Lian M, Gielis J, Niklas KJ, Annals of the New York Academy of Sciences 1524, 118 (2023). http://doi.org/10.1111/NYAS.15000
Abstract: Egg geometry can be described using Preston's equation, which has seldom been used to calculate egg volume (V) and surface area (S) to explore S versus V scaling relationships. Herein, we provide an explicit re-expression of Preston's equation (designated as EPE) to calculate V and S, assuming that an egg is a solid of revolution. The side (longitudinal) profiles of 2221 eggs of six avian species were digitized, and the EPE was used to describe each egg profile. The volumes of 486 eggs from two avian species predicted by the EPE were compared with those obtained using water displacement in graduated cylinders. There was no significant difference in V using the two methods, which verified the utility of the EPE and the hypothesis that eggs are solids of revolution. The data also indicated that V is proportional to the product of egg length (L) and maximum width (W) squared. A 2/3-power scaling relationship between S and V for each species was observed, that is, S is proportional to (LW2)(2/3). These results can be extended to describe the shapes of the eggs of other species to study the evolution of avian (and perhaps reptilian) eggs.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
Impact Factor: 5.2
DOI: 10.1111/NYAS.15000
|
|
|
“About “bulky” links, generated by generalized Möbius-Listing bodies”. Gielis J, Tavkelidze I, Ricci PE page 115 (2011).
Keywords: H3 Book chapter; Sustainable Energy, Air and Water Technology (DuEL)
|
|
|
“The Dirichlet problem for the Laplace equation in supershaped annuli”. Caratelli D, Gielis J, Tavkhelidze I, Ricci PE, Boundary value problems , 113 (2013). http://doi.org/10.1186/1687-2770-2013-113
Abstract: The Dirichlet problem for the Laplace equation in normal-polar annuli is addressed by using a suitable Fourier-like technique. Attention is in particular focused on the wide class of domains whose boundaries are defined by the so-called superformula introduced by Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica© is developed in order to validate the proposed methodology. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1186/1687-2770-2013-113
|
|
|
“Advanced particle swarm optimization methods for electromagnetics”. Mescia L, Bia P, Gielis J, Caratelli D, , 109 (2023). http://doi.org/10.55060/s.atmps.231115.010
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.
Keywords: P1 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.55060/s.atmps.231115.010
|
|