Abstract: The relationship between spatial density and size of plants is an important topic in plant ecology. The self-thinning rule suggests a −3/2 power between average biomass and density or a −1/2 power between stand yield and density. However, the self-thinning rule based on total leaf area per plant and density of plants has been neglected presumably because of the lack of a method that can accurately estimate the total leaf area per plant. We aimed to find the relationship between spatial density of plants and total leaf area per plant. We also attempted to provide a novel model for accurately describing the leaf shape of bamboos. We proposed a simplified Gielis equation with only two parameters to describe the leaf shape of bamboos one model parameter represented the overall ratio of leaf width to leaf length. Using this method, we compared some leaf parameters (leaf shape, number of leaves per plant, ratio of total leaf weight to aboveground weight per plant, and total leaf area per plant) of four bamboo species of genus Indocalamus Nakai (I. pedalis (Keng) P.C. Keng, I. pumilus Q.H. Dai and C.F. Keng, I. barbatus McClure, and I. victorialis P.C. Keng). We also explored the possible correlation between spatial density and total leaf area per plant using log-linear regression. We found that the simplified Gielis equation fit the leaf shape of four bamboo species very well. Although all these four species belonged to the same genus, there were still significant differences in leaf shape. Significant differences also existed in leaf area per plant, ratio of leaf weight to aboveground weight per plant, and leaf length. In addition, we found that the total leaf area per plant decreased with increased spatial density. Therefore, we directly demonstrated the self-thinning rule to improve light interception.

Abstract: Recently, a universal equation by Narushin, Romanov, and Griffin (hereafter, the NRGE) was proposed to describe the shape of avian eggs. While NRGE can simulate the shape of spherical, ellipsoidal, ovoidal, and pyriform eggs, its predictions were not tested against actual data. Here, we tested the validity of the NRGE by fitting actual data of egg shapes and compared this with the predictions of our simpler model for egg shape (hereafter, the SGE). The eggs of nine bird species were sampled for this purpose. NRGE was found to fit the empirical data of egg shape well, but it did not define the egg length axis (i.e., the rotational symmetric axis), which significantly affected the prediction accuracy. The egg length axis under the NRGE is defined as the maximum distance between two points on the scanned perimeter of the egg's shape. In contrast, the SGE fitted the empirical data better, and had a smaller root-mean-square error than the NRGE for each of the nine eggs. Based on its mathematical simplicity and goodness-of-fit, the SGE appears to be a reliable and useful model for describing egg shape.

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.

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.

Abstract: Plant leaves exhibit diverse shapes that enable them to utilize a light resource maximally. If there were a general parametric model that could be used to calculate leaf area for different leaf shapes, it would help to elucidate the adaptive evolutional link among plants with the same or similar leaf shapes. We propose a simplified version of the original Gielis equation (SGE), which was developed to describe a variety of object shapes ranging from a droplet to an arbitrary polygon. We used this equation to fit the leaf profiles of 53 species (among which, 48 bamboo plants, 5 woody plants, and 10 geographical populations of a woody plant), totaling 3310 leaves. A third parameter (namely, the floating ratio c in leaf length) was introduced to account for the case when the theoretical leaf length deviates from the observed leaf length. For most datasets, the estimates of c were greater than zero but less than 10%, indicating that the leaf length predicted by the SGE was usually smaller than the actual length. However, the predicted leaf areas approximated their actual values after considering the floating ratios in leaf length. For most datasets, the mean percent errors of leaf areas were lower than 6%, except for a pooled dataset with 42 bamboo species. For the elliptical, lanceolate, linear, obovate, and ovate shapes, although the SGE did not fit the leaf edge perfectly, after adjusting the parameter c, there were small deviations of the predicted leaf areas from the actual values. This illustrates that leaves with different shapes might have similar functional features for photosynthesis, since the leaf areas can be described by the same equation. The anisotropy expressed as a difference in leaf shape for some plants might be an adaptive response to enable them to adapt to different habitats.

Abstract: Leaf shape is closely related to economics of leaf support and leaf functions, including light interception, water use, and CO2 uptake, so correct quantification of leaf shape is helpful for studies of leaf structure/function relationships. There are some extant indices for quantifying leaf shape, including the leaf width/length ratio (W/L), leaf shape fractal dimension (FD), leaf dissection index, leaf roundness index, standardized bilateral symmetrical index, etc. W/L ratio is the simplest to calculate, and recent studies have shown the importance of the W/L ratio in explaining the scaling exponent of leaf dry mass vs. leaf surface area and that of leaf surface area vs. leaf length. Nevertheless, whether the W/L ratio could reflect sufficient geometrical information of leaf shape has been not tested. The FD might be the most accurate measure for the complexity of leaf shape because it can characterize the extent of the self-similarity and other planar geometrical features of leaf shape. However, it is unknown how strongly different indices of leaf shape complexity correlate with each other, especially whether W/L ratio and FD are highly correlated. In this study, the leaves of nine Magnoliaceae species (>140 leaves for each species) were chosen for the study. We calculated the FD value for each leaf using the box-counting approach, and measured leaf fresh mass, surface area, perimeter, length, and width. We found that FD is significantly correlated to the W/L ratio and leaf length. However, the correlation between FD and the W/L ratio was far stronger than that between FD and leaf length for each of the nine species. There were no strong correlations between FD and other leaf characteristics, including leaf area, ratio of leaf perimeter to area, fresh mass, ratio of leaf fresh mass to area, and leaf roundness index. Given the strong correlation between FD and W/L, we suggest that the simpler index, W/L ratio, can provide sufficient information of leaf shape for similarly-shaped leaves. Future studies are needed to characterize the relationships among FD and W/L in leaves with strongly varying shape, e.g., in highly dissected leaves.

Abstract: Previous studies have shown that positron-annihilation spectroscopy is a highly sensitive probe of the electronic structure and surface composition of ligand-capped semiconductor quantum dots (QDs) embedded in thin films. The nature of the associated positron state, however, whether the positron is confined inside the QDs or localized at their surfaces, has so far remained unresolved. Our positron-annihilation lifetime spectroscopy studies of CdSe QDs reveal the presence of a strong lifetime component in the narrow range of 358–371 ps, indicating abundant trapping and annihilation of positrons at the surfaces of the QDs. Furthermore, our ab initio calculations of the positron wave function and lifetime employing a recent formulation of the weighted density approximation demonstrate the presence of a positron surface state and predict positron lifetimes close to experimental values. Our study thus resolves the long-standing question regarding the nature of the positron state in semiconductor QDs and opens the way to extract quantitative information on surface composition and ligand-surface interactions of colloidal semiconductor QDs through highly sensitive positron-annihilation techniques.

Abstract: Three-dimensional (3D) computational fluid dynamics (CFD) simulations were performed to study solids flow dynamics and solids back-mixing behavior in a screw reactor (designed for thermal conversion of dry biomass particles) based on the Eulerian-Eulerian method. Simulation results were compared against experimental data with respect to filling degree and mean residence time of particles. The mean deviations for filling degree and for mean residence time between simulation and experiment were about 0.01 and 11.4 s, respectively, which shows that the model is reasonably accurate in predicting solids flow behavior in the screw reactor. The solids flow dynamics inside the reactor were discussed. The solids residence time distribution (RTD) was calculated and the degree of solids back-mixing in the forward transportation direction of the reactor was analyzed. It was found that solids being flung over the shaft and solids back-leakage, resulting from the low solids forward transportation velocity at the clearance between the flight and the bottom shell of the screw reactor, were responsible for solids back-mixing. The degree of solids back-mixing can be reduced at higher screw rotating speeds when keeping inlet mass flow rate of solids constant. (C) 2019 Elsevier Ltd. All rights reserved.

Abstract: tWe investigated the plasma-assisted catalytic reactions for the production of value-added chemicalsfrom Ni-catalyzed plasma dry reforming of methane by means of density functional theory (DFT). Weinspected many activation barriers, from the early stage of adsorption of the major chemical fragmentsderived fromCH4andCO2molecules up to the formation of value-added chemicals at the surface, focusingon the formation of methanol, as well as the hydrogenation of C1and C2hydrocarbon fragments. Theactivation barrier calculations show that the presence of surface-bound H atoms and in some cases alsoremaining chemical fragments at the surface facilitates the formation of products. This implies that thehydrogenation of a chemical fragment on the hydrogenated crystalline surface is energetically favouredcompared to the simple hydrogenation of the chemical fragment at the bare Ni(111) surface. Indeed, thepresence of hydrogen modifies the electronic structure of the surface and the course of the reactions.We therefore conclude that surface-bound H atoms, and to some extent also the remaining chemicalfragments at the crystalline surface, induce the following effects: they facilitate associative desorption ofmethanol and ethane by increasing the rate of H-transfer to the adsorbed fragments while they impedehydrogenation of ethylene to ethane, thus promoting again the desorption of ethylene. Overall, they thusfacilitate the catalytic conversion of the formed fragments from CH4and CO2, into value-added chemicals.Finally, we believe that the retention of methane fragments, especially CH3, in the presence of surface-boundHatoms (as observed here for Ni) can be regarded as an identifier for the proper choice of a catalystfor the production of value-added chemicals.