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.

Abstract: Plants have diverse leaf shapes that have evolved to adapt to the environments they have experienced over their evolutionary history. Leaf shape and leaf size can greatly influence the growth rate, competitive ability, and productivity of plants. However, researchers have long struggled to decide how to properly quantify the complexity of leaf shape. Prior studies recommended the leaf roundness index (RI = 4πA/P2) or dissection index (DI = ), where P is leaf perimeter and A is leaf area. However, these two indices merely measure the extent of the deviation of leaf shape from a circle, which is usually invalid as leaves are seldom circular. In this study, we proposed a simple measure, named the ellipticalness index (EI), for quantifying the complexity of leaf shape based on the hypothesis that the shape of any oval leaf can be regarded as a variation from a standard ellipse. 2220 leaves from nine species of Magnoliaceae were sampled to check the validity of the EI. We also tested the validity of the Montgomery equation (ME), which assumes a proportional relationship between leaf area and the product of leaf length and width, because the EI actually comes from the proportionality coefficient of the ME. We also compared the ME with five other models of leaf area. The ME was found to be the best model for calculating leaf area based on consideration of the trade-off between model fit vs. complexity, which strongly supported the robustness of the EI for describing oval leaf shape. The new index can account for both leaf shape and size, and we conclude that it is a promising method for quantifying and comparing oval leaf shapes across species in future studies.

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.

Abstract: In this report we describe the basics of biological carbon fixation in bamboo forests. Confusing carbon stock with carbon flux has led to false expectations on the significance of bamboo forests as carbon sinks. Furthermore, misunderstandings about the growth of bamboo culms can lead to highly exaggerated expectations on the productivity of bamboo.

Abstract: In the present work, multiphysics modeling was used to investigate the feasibility of a photocatalysis-based outdoor air purifying solution that could be used in high polluted streets, especially street canyons. The article focuses on the use of a semi-active photocatalysis in the surfaces of the street as a solution to remove anthropogenic pollutants from the air. The solution is based on lamellae arranged horizontally on the wall of the street, coated with a photocatalyst (TiO2), lightened with UV light, with a dimension of 8 cm × 48 cm × 1 m. Fans were used in the system to create airflow. A high purification percentage was obtained. An artificial neural network (ANN) was used to predict the optimal purification method based on previous simulations, to design purification strategies considering the energy cost. The ANN was used to forecast the amount of purified with a feed-forward neural network and a backpropagation algorithm to train the model.

Abstract: The implementation of nitritation/denitritation (Nit/DNit) as alternative to nitrification/denitrification (N/DN) is driven by operational cost savings, e.g. 1.0-1.8 EUR/ton slurry treated. However, as for any biological nitrogen removal process, Nit/DNit can emit the potent greenhouse gas nitrous oxide (N2O). Challenges remain in understanding formation mechanisms and in mitigating the emissions, particularly at a low ratio of organic carbon consumption to nitrogen removal (CODrem/N-rem). In this study, the centrate (centrifuge supernatant) from anaerobic co-digestion of pig slurry was treated in a sequencing batch reactor. The process removed approximately 100% of ammonium a satisfactory nitrogen loading rate (0.4 g N/L/d), with minimum nitrite and nitrate in the effluent. Substantial N2O emission (around 17% of the ammonium nitrogen loading) was observed at the baseline operational condition (dissolved oxygen, DO, levels averaged at 0.85 mg O-2/L; CODrem/N-rem of 2.8) with similar to 68% of the total emission contributed by nitritation. Emissions increased with higher nitrite accumulation and lower organic carbon to nitrogen ratio. Yet, higher DO levels (similar to 2.2 mg O-2/L) lowered the aerobic N2O emission and weakened the dependency on nitrite concentration, suggesting a shift in N2O production pathway. The most effective N2O mitigation strategy combined intermittent patterns of aeration, anoxic feeding and anoxic carbon dosage, decreasing emission by over 99% (down to similar to 0.12% of the ammonium nitrogen loading). Without anaerobic digestion, mitigated Nit/DNit decreases the operational carbon footprint with about 80% compared to N/DN. With anaerobic digestion included, about 4 times more carbon is sequestered. In conclusion, the low CODrem/N-rem feature of Nit/DNit no longer offsets its environmental sustainability provided the process is smartly operated. (c) 2017 Elsevier Ltd. All rights reserved.

Abstract: Although many fruit geometries resemble a solid of revolution, this assumption has rarely been rigorously examined. To test this assumption, 574 fruits of Canarium album (Lour.) DC. which appear to have an ellipsoidal shape, were examined to determine the validity of a general avian-based egg-shape equation, referred to as the explicit Preston equation (EPE). The assumption that the C. album fruit geometry is a solid of revolution is tested by applying the volume formula for a solid of revolution using the EPE. The goodness of fit of the EPE was assessed using the adjusted root-mean-square error (RMSEadj). The relationship between the observed volume (Vobs) of each fruit, as measured by water displacement in a graduated cylinder, and the predicted volumes (Vpre) based on the EPE was also evaluated using the equation Vpre = slope * Vobs. All the RMSEadj values were smaller than 0.05, which demonstrated the validity of the EPE based on C. album fruit profiles. The 95% confidence interval of the slope of Vpre vs. Vobs included 1.0, indicating that there was no significant difference between Vpre and Vobs. The data confirm that C. album fruits are solids of revolution. This study provides a new approach for calculating the volume and surface area of geometrically similar fruits, which can be extended to other species with similar fruit geometries to further explore the ontogeny and evolution of angiosperm reproductive organs.

Abstract: Stomata are essential for the exchange of water vapour and atmospheric gases between vascular plants and their external environments. The stomatal geometries of many plants appear to be elliptical. However, prior studies have not tested whether this is a mathematical reality, particularly since many natural shapes that appear to be ellipses are superellipses with greater or smaller edge curvature than predicted for an ellipse. Compared with the ellipse equation, the superellipse equation includes an additional parameter that allows generation of a larger range of shapes. We randomly selected 240 stomata from each of four Magnoliaceae species to test whether the stomatal geometries are superellipses or ellipses. The stomatal geometries for most stomata (943/960) were found to be described better using the superellipse equation. The traditional “elliptical stomata hypothesis” resulted in an underestimation of the area of stomata, whereas the superellipse equation accurately predicted stomatal area. This finding has important implications for the estimation of stomatal area in studies looking at stomatal shape, geometry, and function.

Abstract: Films of close-packed Au nanoparticles are coupled electrodynamically through their collective plasmon resonances. This collective optical response results in enhanced light–matter interactions, which can be exploited in various applications. Here, we demonstrate their application in sensing volatile organic compounds, using methanol as a test case. Ordered films over several cm2 were obtained by interfacial self-assembly of colloidal Au nanoparticles (∼10 nm diameter) through controlled evaporation of the solvent. Even though isolated nanoparticles of this size are inherently nonscattering, when arranged in a close-packed film the plasmonic coupling results in a strong reflectance and absorbance. The in situ tracking of vapor phase methanol concentration through UV–vis transmission measurements of the nanoparticle film is first demonstrated. Next, in situ ellipsometry of the self-assembled films in the Kretschmann (also known as ATR) configuration is shown to yield enhanced sensitivity, especially with phase difference measurements, Δ. Our study shows the excellent agreement between theoretical models of the spectral response of self-assembled films with experimental in situ sensing experiments. At the same time, the theoretical framework provides the basis for the interpretation of the various observed experimental trends. Combining periodic nanoparticle films with ellipsometry in the Kretschmann configuration is a promising strategy toward highly sensitive and selective plasmonic thin-film devices based on colloidal fabrication methods for volatile organic compound (VOC) sensing applications.