Tissue growth constrains root organ outlines into an isometrically scalable shape

ABSTRACTOrgan morphologies are diverse but also conserved under shared developmental constraints among species. Any geometrical similarities in the shape behind diversity and the underlying developmental constraints remain unclear. Plant root tip outlines commonly exhibit a dome shape, which likely performs physiological functions, despite the diversity in size and cellular organization among distinct root classes and/or species. We carried out morphometric analysis of the primary roots of ten angiosperm species and of the lateral roots (LRs) of Arabidopsis, and found that each root outline was isometrically scaled onto a parameter-free catenary curve, a stable structure adopted for arch bridges. Using the physical model for bridges, we analogized that localized and spatially uniform occurrence of oriented cell division and expansion force the LR primordia (LRP) tip to form a catenary curve. These growth rules for the catenary curve were verified by tissue growth simulation of developing LRP development based on time-lapse imaging. Consistently, LRP outlines of mutants compromised in these rules were found to deviate from catenary curves. Our analyses demonstrate that physics-inspired growth rules constrain plant root tips to form isometrically scalable catenary curves.

6. and beyond, to complex things

‘ … and beyond, to complex things’ first considers the Taylor series for the exponential function. One of the most famous, yet enigmatic, numbers in mathematics, e is an irrational number equal to 2.718281828. … Exponential functions deal with the phenomena of growth and decay. As calculus was starting to become established, curious parallels between the apparently disparate worlds of trigonometry and exponential functions were starting to appear. Imaginary numbers, Euler’s formula, and Euler’s identity are discussed along with the Argand diagram, De Moivre’s formula, hyperbolic trigonometric functions, and the catenary curve. Imaginary numbers are now at the heart of science and technology, and are used in the study of electromagnetic waves, cellular and wireless technologies, and fluid dynamics.

LiDAR-Based Real-Time Detection and Modeling of Power Lines for Unmanned Aerial Vehicles

The effective monitoring and maintenance of power lines are becoming increasingly important due to a global growing dependence on electricity. The costs and risks associated with the traditional foot patrol and helicopter-based inspections can be reduced by using UAVs with the appropriate sensors. However, this implies developing algorithms to make the power line inspection process reliable and autonomous. In order to overcome the limitations of visual methods in the presence of poor light and noisy backgrounds, we propose to address the problem of power line detection and modeling based on LiDAR. The PL 2 DM, Power Line LiDAR-based Detection and Modeling, is a novel approach to detect power lines. Its basis is a scan-by-scan adaptive neighbor minimalist comparison for all the points in a point cloud. The power line final model is obtained by matching and grouping several line segments, using their collinearity properties. Horizontally, the power lines are modeled as a straight line, and vertically as a catenary curve. Using a real dataset, the algorithm showed promising results both in terms of outputs and processing time, adding real-time object-based perception capabilities for other layers of processing.

Calculation of magnetic field intensity under power line with taking into account conductor sag

The paper presents a calculation method of the magnetic field under an overhead power line taking into account conductor sag, which is described by the catenary curve. The calculations take into account the variability of the charge distribution along the conductor and wire sag for the eclectic field, while the calculation of intensity of the magnetic field take into account the impact of induced currents in the wires of lightning. The simulation results were compared with results measurements.

Effect of Boat Tail Profile on Drag Coefficient of a Sedan Using CFD

An appendage is a boat tail which is installed at the rear section of the passenger car. An inflatable appendage has been developed to reduce the aerodynamic drag experienced by passenger cars. It can be inflated when driving under high-speed conditions and deflated while parking. In this study, an appendage is designed to maintain the streamlined rear body configuration and reduce flow separation. The profile of this aerodynamic device is based on several mathematical curves such as kappa curve, lame curve, catenary curve and aerofoil curve. Four types of boat tailing devices with different lengths and profiles were installed, and computational fluid dynamics (CFD) analysis was performed under moving ground conditions. The primary objective of this study is to find an optimum shape for the appendage and explain the aerodynamic drag reduction mechanism. Comparisons between the base model and modified models were made on the basis of the coefficient of drag, pressure contours, velocity contours, velocity streamlines and pressure distribution plot. It is shown that significant drag reduction can be obtained with the proposed aerodynamic device. Improvement in fuel efficiency varies based on the profile of add-on device. It is shown numerically that the aerodynamic performance is improved by 18.8% compared to the base model. As a result, the fuel consumption of the modified sedan reduces by 4.5%.