“A note on spirals and curvature”. Gielis J, Caratelli D, Shi P, Ricci PE, Growth and form 1, 1 (2020). http://doi.org/10.2991/GAF.K.200124.001
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.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.2991/GAF.K.200124.001
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“Following the photons route : mathematical models describing the interaction of diatoms with light”. De Tommasi E, Rogato A, Caratelli D, Mescia L, Gielis J page 1 (2022).
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.
Keywords: H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
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“Universal equations : a fresh perspective”. Gielis J, Shi P, Caratelli D, Growth and Form (2022)
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
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
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“A biogeometrical model for corolla fusion in Asclepiad flowers”. Gielis J, Caratelli D, Fougerolle Y, Ricci PE, Gerats T page 83 (2017).
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.
Keywords: H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.2991/978-94-6239-261-8_7
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“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)
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“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
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“Electromagnetic characterization of supershaped lens antennas for high-frequency applications”. Bia P, Caratelli D, Mescia L, Gielis J page 1679 (2013).
Keywords: H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
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“Fourier-like solution of the Dirichlet problem for the Laplace Equation in k-type Gielis domains”. Caratelli D, Gielis J, Ricci PE, Journal of pure and applied mathematics : advances and applications 5, 99 (2011)
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.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
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“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
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“Lamé-Gielis curves in biology and geometry”. Gielis J, Shi P, Beirinckx B, Caratelli D, Ricci PE, (2021)
Keywords: P3 Proceeding; Sustainable Energy, Air and Water Technology (DuEL)
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“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
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“Some properties of “bulky&rdquo, links, generated by Generalized Möbius Listing's bodies GML4n”. Caratelli D, Gielis J, Ricci PE, Tavkhelidze I, (2013)
Keywords: P3 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
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“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
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“Optimization of gate-on-source-only tunnel FETs with counter-doped pockets”. Kao K-H, Verhulst AS, Vandenberghe WG, Sorée B, Magnus W, Leonelli D, Groeseneken G, De Meyer K, IEEE transactions on electron devices 59, 2070 (2012). http://doi.org/10.1109/TED.2012.2200489
Abstract: We investigate a promising tunnel FET configuration having a gate on the source only, which is simultaneously exhibiting a steeper subthreshold slope and a higher ON-current than the lateral tunneling configuration with a gate on the channel. Our analysis is performed based on a recently developed 2-D quantum-mechanical simulator calculating band-to-band tunneling and including quantum confinement (QC). It is shown that the two disadvantages of the structure, namely, the sensitivity to gate alignment and the physical oxide thickness, are mitigated by placing a counter-doped parallel pocket underneath the gate-source overlap. The pocket also significantly reduces the field-induced QC. The findings are illustrated with all-Si and all-Ge gate-on-source-only tunnel field-effect transistor simulations.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 2.605
Times cited: 72
DOI: 10.1109/TED.2012.2200489
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“Anisotropic magnetism and spin-dependent transport in Co nanoparticle embedded ZnO thin films”. Li DY, Zeng YJ, Pereira LMC, Batuk D, Hadermann J, Zhang YZ, Ye ZZ, Temst K, Vantomme A, Van Bael MJ, Van Haesendonck C;, Journal of applied physics 114, 033909 (2013). http://doi.org/10.1063/1.4815877
Abstract: Oriented Co nanoparticles were obtained by Co ion implantation in crystalline ZnO thin films grown by pulsed laser deposition. Transmission electron microscopy revealed the presence of elliptically shaped Co precipitates with nanometer size, which are embedded in the ZnO thin films, resulting in anisotropic magnetic behavior. The low-temperature resistance of the Co-implanted ZnO thin films follows the Efros-Shklovskii type variable-range-hopping. Large negative magnetoresistance (MR) exceeding 10% is observed in a magnetic field of 1 T at 2.5K and the negative MR survives up to 250K (0.3%). The negative MR reveals hysteresis as well as anisotropy that correlate well with the magnetic properties, clearly demonstrating the presence of spin-dependent transport. (C) 2013 AIP Publishing LLC.
Keywords: A1 Journal article; Electron microscopy for materials research (EMAT)
Impact Factor: 2.068
Times cited: 10
DOI: 10.1063/1.4815877
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“Modeling the single-gate, double-gate, and gate-all-around tunnel field-effect transistor”. Verhulst A, Sorée B, Leonelli D, Vandenberghe WG, Groeseneken G, Journal Of Applied Physics 107, 024518 (2010). http://doi.org/10.1063/1.3277044
Abstract: Tunnel field-effect transistors (TFETs) are potential successors of metal-oxide-semiconductor FETs because scaling the supply voltage below 1 V is possible due to the absence of a subthreshold-swing limit of 60 mV/decade. The modeling of the TFET performance, however, is still preliminary. We have developed models allowing a direct comparison between the single-gate, double-gate, and gate-all-around configuration at high drain voltage, when the drain-voltage dependence is negligible, and we provide improved insight in the TFET physics. The dependence of the tunnel current on device parameters is analyzed, in particular, the scaling with gate-dielectric thickness, channel thickness, and dielectric constants of gate dielectric and channel material. We show that scaling the gate-dielectric thickness improves the TFET performance more than scaling the channel thickness and that improvements are often overestimated. There is qualitative agreement between our model and our experimental data.
Keywords: A1 Journal article; Electron Microscopy for Materials Science (EMAT);
Impact Factor: 2.068
Times cited: 150
DOI: 10.1063/1.3277044
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“A facile synthesis of Ag@PdAg core-shell architecture for efficient purification of ethene feedstock”. Ma R, He Y, Feng J, Hu Z-Y, Van Tendeloo G, Li D, Journal of catalysis 369, 440 (2019). http://doi.org/10.1016/J.JCAT.2018.11.037
Abstract: Precise control of elemental configurations within multimetallic nanoparticles could enable access to functional nanomaterials with significant performance benefits. Here, we present a one-pot synthesis of supported Ag@PdAg core-shell catalyst with an ordered PdAg alloy shell and an Ag core. Both the relative reduction potential and ratio of metal precursors are essential for this synthesis strategy. The distinguished properties of Ag@PdAg, particularly the electronic structure, indicates the existence of electron modification not only between Pd and Ag on PdAg shell, but between Ag core and alloy shell. The Ag@PdAg catalyst displays 97% ethene yield in the partial hydrogenation of acetylene, which is 2.0 and 8.1 times that of over PdAg alloy and pure Pd catalysts, and this is the most selective catalyst reported to data under industrial evaluation conditions. Moreover, this core-shell structure exhibits preferable stability with comparison to PdAg alloy catalyst. The facile synthesis of core-shell architecture with alloy shell structure provides a new platform for efficient catalytic transfer of chemical resource. (C) 2018 Elsevier Inc. All rights reserved.
Keywords: A1 Journal article; Electron microscopy for materials research (EMAT)
DOI: 10.1016/J.JCAT.2018.11.037
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“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
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“Electromagnetic mathematical modeling of 3D supershaped dielectric lens antennas”. Mescia L, Bia P, Caratelli D, Chiapperino MA, Stukach O, Gielis J, Mathematical problems in engineering: theory, methods, and applications , 8130160 (2016). http://doi.org/10.1155/2016/8130160
Abstract: The electromagnetic analysis of a special class of 3D dielectric lens antennas is described in detail. This new class of lens antennas has a geometrical shape defined by the three-dimensional extension of Gielis formula. The analytical description of the lens shape allows the development of a dedicated semianalytical hybrid modeling approach based on geometrical tube tracing and physical optic. In order to increase the accuracy of the model, the multiple reflections occurring within the lens are also taken into account.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1155/2016/8130160
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“Some properties of “bulky&rdquo, links, generated by Generalized Möbius Listing's bodies GML4n”. Caratelli D, Gielis J, Ricci PE, Tavkhelidze I, Journal of mathematical sciences 216, 509 (2016). http://doi.org/10.1007/S10958-016-2907-X
Abstract: In the present paper, we consider the bulky knots and bulky links that appear after cutting of generalized MöbiusListing GML 4 n bodies (with corresponding radial cross sections square) along different generalized MöbiusListing surfaces GML 2 n situated in it. The aim of this article is to examine the number and geometric structure of independent objects that appear after such a cutting process of GML 4 n bodies. In most cases, we are able to count the indices of the resulting mathematical objects according to the known tabulation for knots and links of small complexity.
Keywords: A2 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1007/S10958-016-2907-X
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“The Robin problem for the Helmholtz equation in a starlike planar domain”. Caratelli D, Gielis J, Natalini P, Ricci PE, Tavkhelidze I, Georgian mathematical journal 18, 465 (2011). http://doi.org/10.1515/GMJ.2011.0031
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.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1515/GMJ.2011.0031
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“Electromagnetic modeling and design of a novel class of complementary split‐ring resonators”. Martínez-Dueñas EJR, de Jong van Coevorden CM, Stukach OV, Panokin NV, Gielis J, Caratelli D, International journal of RF and microwave computer-aided engineering 29, e21582 (2019). http://doi.org/10.1002/MMCE.21582
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.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1002/MMCE.21582
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“The “Historical Materials BAG&rdquo, : a new facilitated access to synchrotron X-ray diffraction analyses for cultural heritage materials at the European Synchrotron Radiation Facility”. Cotte M, Gonzalez V, Vanmeert F, Monico L, Dejoie C, Burghammer M, Huder L, de Nolf W, Fisher S, Fazlic I, Chauffeton C, Wallez G, Jimenez N, Albert-Tortosa F, Salvado N, Possenti E, Colombo C, Ghirardello M, Comelli D, Avranovich Clerici E, Vivani R, Romani A, Costantino C, Janssens K, Taniguchi Y, McCarthy J, Reichert H, Susini J, Molecules: a journal of synthetic chemistry and natural product chemistry 27, 1997 (2022). http://doi.org/10.3390/MOLECULES27061997
Abstract: The European Synchrotron Radiation Facility (ESRF) has recently commissioned the new Extremely Brilliant Source (EBS). The gain in brightness as well as the continuous development of beamline instruments boosts the beamline performances, in particular in terms of accelerated data acquisition. This has motivated the development of new access modes as an alternative to standard proposals for access to beamtime, in particular via the “block allocation group” (BAG) mode. Here, we present the recently implemented “historical materials BAG”: a community proposal giving to 10 European institutes the opportunity for guaranteed beamtime at two X-ray powder diffraction (XRPD) beamlines-ID13, for 2D high lateral resolution XRPD mapping, and ID22 for high angular resolution XRPD bulk analyses-with a particular focus on applications to cultural heritage. The capabilities offered by these instruments, the specific hardware and software developments to facilitate and speed-up data acquisition and data processing are detailed, and the first results from this new access are illustrated with recent applications to pigments, paintings, ceramics and wood.
Keywords: A1 Journal article; Antwerp X-ray Imaging and Spectroscopy (AXIS)
Impact Factor: 4.6
DOI: 10.3390/MOLECULES27061997
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“On means, polynomials and special functions”. Gielis J, Verhulst R, Caratelli D, Ricci PE, Tavkhelidze I, The teaching of mathematics 17, 1 (2014)
Keywords: A1 Journal article; Educational sciences; Sustainable Energy, Air and Water Technology (DuEL)
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“Unexpected optical response of single ZnO nanowires probed using controllable electrical contacts”. Zeng YI, Menghini M, Li DY, Lin SS, Ye ZZ, Hadermann J, Moorkens T, Seo JW, Locquet J-P, van Haesendonck C, Physical chemistry, chemical physics 13, 6931 (2011). http://doi.org/10.1039/c1cp00012h
Abstract: Relying on combined electron-beam lithography and lift-off methods Au/Ti bilayer electrical contacts were attached to individual ZnO nanowires (NWs) that were grown by a vapor phase deposition method. Reliable Schottky-type as well as ohmic contacts were obtained depending on whether or not an ion milling process was used. The response of the ZnO NWs to ultraviolet light was found to be sensitive to the type of contacts. The intrinsic electronic properties of the ZnO NWs were studied in a field-effect transistor configuration. The transfer characteristics, including gate threshold voltage, hysteresis and operational mode, were demonstrated to unexpectedly respond to visible light. The origin of this effect could be accounted for by the presence of point defects in the ZnO NWs.
Keywords: A1 Journal article; Electron microscopy for materials research (EMAT)
Impact Factor: 4.123
Times cited: 7
DOI: 10.1039/c1cp00012h
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“Plasma-catalytic one-step steam reforming of CH₄, to CH₃OH and H₂, promoted by oligomerized [Cu-O-Cu] species on zeolites”. Fang W, Wang X, Li S, Hao Y, Yang Y, Zhao W, Liu R, Li D, Li C, Gao X, Wang L, Guo H, Yi Y, Green chemistry : cutting-edge research for a greener sustainable future 26, 5150 (2024). http://doi.org/10.1039/D4GC00265B
Abstract: Oligomerized [Cu-O-Cu] species are reported to be efficient in promoting plasma catalytic one-step steam reforming of methane to methanol and hydrogen, achieving 6.8% CH4 conversion and 73.1% CH3OH selectivity without CO2.
Keywords: A1 Journal article; Engineering sciences. Technology; Plasma Lab for Applications in Sustainability and Medicine – Antwerp (PLASMANT)
Impact Factor: 9.8
DOI: 10.1039/D4GC00265B
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“Combined use of synchrotron-radiation-based imaging techniques for the characterization of structured catalysts”. Basile F, Benito P, Bugani S, de Nolf W, Fornasari G, Janssens K, Morselli L, Scavetta E, Tonelli D, Vaccari A, Advanced functional materials 20, 4117 (2010). http://doi.org/10.1002/ADFM.201001004
Abstract: Active-phase-coated metallic supports as structured catalysts are gaining attention in endothermic and exothermic processes because they improve heat transfer. The deposition of a well-adhered and stable catalyst layer on the metallic support constitutes an important feature for the successful application of the final material. In this work, coating of FeCrAlY foams is performed by a one-step electrosynthesis-deposition of hydrotalcite-type compounds, precursors of catalysts active in endothermic steam methane reforming. The catalysts are studied at different length scales by using, for the first time, a combination of several techniques: SEM/EDS and X-ray fluorescence, X-ray powder diffraction and absorption-tomography experiments on the micro- and nanoscales at a synchrotron facility. The results show that the morphology of the coating depends on the synthesis conditions and that the catalyst may be described as Ni metal crystallites dispersed on γ-Al2O3, homogeneously coating the FeCrAlY foam.
Keywords: A1 Journal article; AXES (Antwerp X-ray Analysis, Electrochemistry and Speciation)
Impact Factor: 12.124
Times cited: 24
DOI: 10.1002/ADFM.201001004
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“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
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“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
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“Application of Gielis transformation to the design of metamaterial structures”. de Jong van Coevorden CM, Gielis J, Caratelli D, Journal of physics : conference series 963, Unsp 012008 (2018). http://doi.org/10.1088/1742-6596/963/1/012008
Abstract: In this communication, the use of Gielis transformation to design more compact metamaterial unit cells is explored. For this purpose, transformed complementary split ring resonators and spiral resonators are coupled to micro-strip lines and theirbehaviour is investigated. The obtained results confirm that the useof the considered class of supershaped geometries enables the synthesis of very compact scalable microwave components.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1088/1742-6596/963/1/012008
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