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\"Charles Darwin was driven to distraction by plant spirals, growing so exasperated that he once begged a friend to explain the mystery \"if you wish to save me from a miserable death.\" The legendary naturalist was hardly alone in feeling tormented by these patterns. Plant spirals captured the gaze of Leonardo da Vinci and became Alan Turing's final obsession. This book tells the stories of the physicists, mathematicians, and biologists who found themselves magnetically drawn to Fibonacci spirals in plants, seeking an answer to why these beautiful and seductive patterns occur in botanical forms as diverse as pine cones, cabbages, and sunflowers. Do Plants Know Math? takes you down through the centuries to explore how great minds have been captivated and mystified by Fibonacci patterns in nature. It presents a powerful new geometrical solution, little known outside of scientific circles, that sheds light on why regular and irregular spiral patterns occur. Along the way, the book discusses related plant geometries such as fractals and the fascinating way that leaves are folded inside of buds. Your neurons will crackle as you begin to see the connections. The book will inspire you to look at botanical patterns-and the natural world itself-with new eyes. Featuring hundreds of gorgeous color images, Do Plants Know Math? includes a dozen creative hands-on activities and even spiral-plant recipes, encouraging readers to explore and celebrate these beguiling patterns for themselves\"--Publisher's description.

In the present study the mechanisms of evolution of propeller tip and hub vortices in the transitional region and the far field are investigated experimentally. The experiments involved detailed time-resolved visualizations and velocimetry measurements and were aimed at examining the effect of the spiral-to-spiral distance on the mechanisms of wake evolution and instability transition. In this regard, three propellers having the same blade geometry but different number of blades were considered. The study outlined dependence of the wake instability on the spiral-to-spiral distance and, in particular, a streamwise displacement of the transition region at the increasing inter-spiral distance. Furthermore, a multi-step grouping mechanism among tip vortices was highlighted and discussed. It is shown that such a phenomenon is driven by the mutual inductance between adjacent spirals whose characteristics change by changing the number of blades.

The spatio-temporal evolution of a turbulent swirling jet undergoing vortex breakdown has been investigated. Experiments suggest the existence of a self-excited global mode having a single dominant frequency. This oscillatory mode is shown to be absolutely unstable and leads to a rotating counter-winding helical structure that is located at the periphery of the recirculation zone. The resulting time-periodic 3D velocity field is predicted theoretically as being the most unstable mode determined by parabolized stability analysis employing the mean flow data from experiments. The 3D oscillatory flow is constructed from uncorrelated 2D snapshots of particle image velocimetry data, using proper orthogonal decomposition, a phase-averaging technique and an azimuthal symmetry associated with helical structures. Stability-derived modes and empirically derived modes correspond remarkably well, yielding prototypical coherent structures that dominate the investigated flow region. The proposed method of constructing 3D time-periodic velocity fields from uncorrelated 2D data is applicable to a large class of turbulent shear flows.

We report the creation of a nanoscale electrochemical device inside a transmission electron microscope--consisting of a single tin dioxide (SnO₂) nanowire anode, an ionic liquid electrolyte, and a bulk lithium cobalt dioxide (LiCoO₂) cathode--and the in situ observation of the lithiation of the SnO₂ nanowire during electrochemical charging. Upon charging, a reaction front propagated progressively along the nanowire, causing the nanowire to swell, elongate, and spiral. The reaction front is a \"Medusa zone\" containing a high density of mobile dislocations, which are continuously nucleated and absorbed at the moving front. This dislocation cloud indicates large in-plane misfit stresses and is a structural precursor to electrochemically driven solid-state amorphization. Because lithiation-induced volume expansion, plasticity, and pulverization of electrode materials are the major mechanical effects that plague the performance and lifetime of high-capacity anodes in lithium-ion batteries, our observations provide important mechanistic insight for the design of advanced batteries.

Multifunctional applications of textiles have been limited by the inability to spin important materials into yarns. Generically applicable methods are demonstrated for producing weavable yarns comprising up to 95 weight percent of otherwise unspinnable particulate or nanofiber powders that remain highly functional. Scrolled 50-nanometer-thick carbon nanotube sheets confine these powders in the galleries of irregular scroll sacks whose observed complex structures are related to twist-dependent extension of Archimedean spirals, Fermat spirals, or spiral pairs into scrolls. The strength and electronic connectivity of a small weight fraction of scrolled carbon nanotube sheet enables yarn weaving, sewing, knotting, braiding, and charge collection. This technology is used to make yarns of superconductors, lithium-ion battery materials, graphene ribbons, catalytic nanofibers for fuel cells, and titanium dioxide for photocatalysis.

This article takes a concrete mixer truck actually produced by an enterprise as an example. According to the functions of the three-part spiral blades of the front cone, cylinder, and tail of the mixing drum, combined with theoretical knowledge, the Pro/E software is used to realize the re-realization of the blade spiral. design. A spiral line that is more in line with actual working conditions is derived, which provides a theoretical basis for the design and modeling of spiral blades of concrete mixer trucks.

This study was to quantitatively investigate the role of morphological and functional parameters of the left atrium (LA) and left atrial appendage (LAA) with 256-slice spiral computed tomography (CT) in the recurrence of atrial fibrillation (AF) after radiofrequency ablation (RFA). Eighty-three patients with AF who underwent RFA for the first time were divided into the recurrence (n = 27) and non-recurrence (n = 56) groups. All patients underwent a 256-slice spiral CT examination before the operation. The clinical data and quantitative measurement of the morphology and functional parameters of the LA and LAA were analyzed, including the maximal and minimal volume, ejection fraction and volume, and volume strain of LAA and LA (LAAVmax, LAAVmin, LAAEF, LAAEV, and LAA-VS, LAVmax, LAVmin, LAEF, LAEV and LA-VS, respectively). The CHA2DS2-VASc score and the proportion of patients with heart failure were significantly (P < 0.05) higher in the recurrence than non-recurrence group. The LAAVmax, LAAVmin, LAVmax, LAVmin, LAAV and LAV were all significantly greater in the recurrence than non-recurrence group (P < 0.05), and the perimeter, major and minor axes of LAA orifice and LAA depth were also significantly greater in the recurrence than non-recurrence group. The LAAEF, LAEF and LAA-VS were significantly (P < 0.05) lower in the recurrence than non-recurrence group (P < 0.05). Heart failure, CHA2DS2-VASC score, LAEF, LAV, LAAEF and LAA-VS were univariately significant (P < 0.05) risk factors for AF recurrence after ablation. Multivariate analysis revealed LAAEF (HR: 0.790, 95% CI: 0.657–0.950, P = 0.012) and LAAV (HR: 1.160, 95% CI: 1.095–1.229, P <0.001) to be two significant independent predictors of recurrence. ROC curve analysis showed that LAAEF <44.68% had the highest predictive value for recurrence after radiofrequency ablation, with the sensitivity of 90% and specificity of 67.4%, whereas LAA volume >9.25 ml had the highest predictive value for AF recurrence after RFA, with the sensitivity of 85.2% and specificity of 67.9%. In conclusion, the volume of left atrium, volume and morphology of left atrial appendage have all significantly increased while the ejection fraction and volume strain of left atrium and left atrial appendage have both significantly decreased in recurrence than in non-recurrence after radiofrequency ablation. The ejection fraction and volume of left atrial appendage are significant independent predictors of atrial fibrillation recurrence after radiofrequency ablation.

The leaf-cutting ant Acromyrmex crassispinus is considered an important pest in forest plantations in southern Brazil. This work aimed to study the fungal community associated with A. crassispinus colonies, subjected to treatments with subdoses of granulated baits (sulfluramid), which might reduce the ability of the ants to care for their symbiotic fungus and other fungi (maybe biocontrol fungi) would take over, to prospect for potential biological control agents. Samplings of fungus gardens and dead ants allowed the identification of 195 fungal isolates, distributed in 29 families, 36 genera, and 53 species. The most frequent genera were Trichoderma (49.2%), Penicillium (13.8%), Chaetomium (6.2%), and Fusarium (3.6%). This is the first study that conducted a survey of antagonistic and entomopathogenic fungi to A. crassispinus and its symbiotic fungus, reporting for the first time the occurrence of potential biological control agents. Escovopsis weberi , Fusarium oxysporum , Rhizomucor variabilis , Trichoderma atroviride , Trichoderma harzianum , Trichoderma koningiopsis , and Trichoderma spirale are considered some of the potential biocontrol organisms.

In this study we present a novel six-parameter shape model of the human rib centroidal path using logarithmic spirals. It provides a reduction in parameter space from previous models of overall rib shape, while simultaneously reducing fitting error by 34% and increasing curvature continuity. Furthermore, the model directly utilizes geometric properties such as rib end-to-end span, aspect ratio, rib “skewness”, and inner angle with the spine in its parameterization, making the effects of each parameter on overall shape intuitive and easy to visualize. The model was tested against 2197 rib geometries extracted from CT scans from a population of 100 adult females and males of uniformly distributed ages between 20 and 70. Significant size and shape differences between genders were identified, and shape model utility is demonstrated by the production of statistically average male and female rib shapes for all rib levels. Simulated mechanical loading of the resulting model rib shapes showed that the stiffness of statistically average male and female ribs matched well with the average rib stiffness from each separate population. This in-plane rib shape model can be used to characterize variation in human rib geometry seen throughout the population, including investigation of the overall changes in shape and resultant mechanical properties that ribs undergo during aging or disease progression.