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.

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.

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.

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.

Abstract: Co-rich ZnCoO nanoparticles embedded in wurtzite Zn0.7Co0.3O thin films are grown by pulsed laser deposition on a Si substrate. Local superconductivity with an onset Tc at 5.9 K is demonstrated in the hybrid system. The unexpected superconductivity probably results from Co(3+) in the Co-rich ZnCoO nanoparticles or from the interface between the Co-rich nanoparticles and the Zn0.7Co0.3O matrix.

Abstract: <script type='text/javascript'>document.write(unpmarked('Single-walled carbon nanotubes (SWCNTs) possessing a confined inner space protected by chemically resistant shells are promising for delivery, storage, and desorption of various compounds, as well as carrying out specific reactions. Here, we show that SWCNTs interact with molten mercury dichloride (HgCl2) and guide its transformation into dimercury dichloride (Hg2Cl2) in the cavity. The chemical state of host SWCNTs remains almost unchanged except for a small p-doping from the guest Hg2Cl2 nanocrystals. The density functional theory calculations reveal that the encapsulated HgCl2 molecules become negatively charged and start interacting via chlorine bridges when local concentration increases. This reduces the bonding strength in HgCl2, which facilitates removal of chlorine, finally leading to formation of Hg2Cl2 species. The present work demonstrates that SWCNTs not only serve as a template for growing nanocrystals but also behave as an electron-transfer catalyst in the spatially confined redox reaction by donation of electron density for temporary use by the guests.'));

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.

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.

Abstract: Electroporation technique is widely used in biotechnology and medicine for the transport of various molecules through the membranes of biological cells. Different mathematical models of electroporation have been proposed in the literature to study pore formation in plasma and nuclear membranes. These studies are mainly based on models using a single isolated cell with a canonical shape. In this work, a spacetime (x,y,t) multiphysics model based on quasi-static Maxwells equations and nonlinear Smoluchowskis equation has been developed to investigate the electroporation phenomenon induced by pulsed electric field in multicellular systems having irregularly shape. The dielectric dispersion of the cell compartments such as nuclear and plasmatic membranes, cytoplasm, nucleoplasm and external medium have been incorporated into the numerical algorithm, too. Moreover, the irregular cell shapes have been modeled by using the Gielis transformations.

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.

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

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.

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.

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.