Structure and spacing of cellulose microfibrils in woody cell walls of dicots

The structure of cellulose microfibrils in situ in wood from the dicotyledonous (hardwood) species cherry and birch, and the vascular tissue from sunflower stems, was examined by wide-angle X-ray and neutron scattering (WAXS and WANS) and small-angle neutron scattering (SANS). Deuteration of accessible cellulose chains followed by WANS showed that these chains were packed at similar spacings to crystalline cellulose, consistent with their inclusion in the microfibril dimensions and with a location at the surface of the microfibrils. Using the Scherrer equation and correcting for considerable lateral disorder, the microfibril dimensions of cherry, birch and sunflower microfibrils perpendicular to the [200] crystal plane were estimated as 3.0, 3.4 and 3.3 nm respectively. The lateral dimensions in other directions were more difficult to correct for disorder but appeared to be 3 nm or less. However for cherry and sunflower, the microfibril spacing estimated by SANS was about 4 nm and was insensitive to the presence of moisture. If the microfibril width was 3 nm as estimated by WAXS, the SANS spacing suggests that a non-cellulosic polymer segment might in places separate the aggregated cellulose microfibrils

Rhombic Tilings and Primordia Fronts of Phyllotaxis

We introduce and study properties of phyllotactic and rhombic tilings on the cylin- der. These are discrete sets of points that generalize cylindrical lattices. Rhombic tilings appear as periodic orbits of a discrete dynamical system S that models plant pattern formation by stacking disks of equal radius on the cylinder. This system has the advantage of allowing several disks at the same level, and thus multi-jugate config- urations. We provide partial results toward proving that the attractor for S is entirely composed of rhombic tilings and is a strongly normally attracting branched manifold and conjecture that this attractor persists topologically in nearby systems. A key tool in understanding the geometry of tilings and the dynamics of S is the concept of pri- mordia front, which is a closed ring of tangent disks around the cylinder. We show how fronts determine the dynamics, including transitions of parastichy numbers, and might explain the Fibonacci number of petals often encountered in compositae.Comment: 33 pages, 10 picture

USING THE AUTOMATED RANDOM FOREST APPROACH FOR OBTAINING THE COMPRESSIVE STRENGTH PREDICTION OF RCA

The intricate relationships and cohesiveness among numerous components make the task of designing mixture proportions for high-performance concrete (HPC) a challenging endeavour. Machine learning (ML) algorithms are indeed efficacious in mitigating this predicament. However, their lack of an explicit correlation between mixture proportions and compressive strength renders them opaque black box models. To surpass this constraint, the present research puts forward a semi-empirical methodology that involves the utilization of tactics such as non-dimensionalization and optimization. The methodology proposed exhibits a remarkable level of accuracy in predicting compressive strength across various datasets, exemplifying its all-encompassing applicability to diverse datasets.Furthermore, the exact association furnished by semi-empirical equations is a valuable asset for engineers and researchers operating in this domain, especially concerning their prognostic capabilities. The compressive strength of concrete holds significant importance in designing high-performance concrete, and achieving an optimal mixture proportion necessitates a comprehensive comprehension of the complex interplay among diverse factors, including the type and proportion of cement, water-cement ratio, size and type of aggregate, curing conditions, and admixtures. The semi-empirical approach put forth in this study presents a potential remedy to the intricate undertaking by establishing a more unequivocal correlation between mixture ratios and compressive strength

A New Computationally Efficient Method for Spacing n Points on a Sphere

The problem of equally spacing n points on a sphere is impossible in general, but there are methods that come close to spacing the points equally. The method introduced in this paper uses a spiral that was found using experimental evidence. The resulting spacings are close to theoretical bounds, and the method is computationally efficient for large numbers of points. The method\u27s accuracy ranges from 70% to 86% of the upper bound as n changes

Spherical Fibonacci point sets for illumination integrals

Article first published online: 24 JUL 2013Quasi-Monte Carlo (QMC) methods exhibit a faster convergence rate than that of classic Monte Carlo methods. This feature has made QMC prevalent in image synthesis, where it is frequently used for approximating the value of spherical integrals (e.g. illumination integral). The common approach for generating QMC sampling patterns for spherical integration is to resort to unit square low-discrepancy sequences and map them to the hemisphere. However such an approach is suboptimal as these sequences do not account for the spherical topology and their discrepancy properties on the unit square are impaired by the spherical projection. In this paper we present a strategy for producing high-quality QMC sampling patterns for spherical integration by resorting to spherical Fibonacci point sets. We show that these patterns, when applied to illumination integrals, are very simple to generate and consistently outperform existing approaches, both in terms of root mean square error (RMSE) and image quality. Furthermore, only a single pattern is required to produce an image, thanks to a scrambling scheme performed directly in the spherical domain.FCT - Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) within project PEst-OE/EEI/UI0752/2011

Novel fibonacci and non-fibonacci structure in the sunflower: Results of a citizen science experiment

This citizen science study evaluates the occurrence of Fibonacci structure in the spirals of sunflower (Helianthus annuus) seedheads. This phenomenon has competing biomathematical explanations, and our core premise is that observation of both Fibonacci and non-Fibonacci structure is informative for challenging such models. We collected data on 657 sunflowers. In our most reliable data subset, we evaluated 768 clockwise or anticlockwise parastichy numbers of which 565 were Fibonacci numbers, and a further 67 had Fibonacci structure of a predefined type. We also found more complex Fibonacci structures not previously reported in sunflowers. This is the third, and largest, study in the literature, although the first with explicit and independently checkable inclusion and analysis criteria and fully accessible data. This study systematically reports for the first time, to the best of our knowledge, seedheads without Fibonacci structure. Some of these are approximately Fibonacci, and we found in particular that parastichy numbers equal to one less than a Fibonacci number were present significantly more often than those one more than a Fibonacci number. An unexpected further result of this study was the existence of quasi-regular heads, in which no parastichy number could be definitively assigned