The Laplacian energy of random graphs

Gutman {\it et al.} introduced the concepts of energy \En(G) and Laplacian energy \EnL(G) for a simple graph $G$, and furthermore, they proposed a conjecture that for every graph $G$, \En(G) is not more than \EnL(G). Unfortunately, the conjecture turns out to be incorrect since Liu {\it et al.} and Stevanovi\'c {\it et al.} constructed counterexamples. However, So {\it et al.} verified the conjecture for bipartite graphs. In the present paper, we obtain, for a random graph, the lower and upper bounds of the Laplacian energy, and show that the conjecture is true for almost all graphs.Comment: 14 page

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data

Effect of doping concentration of tunnel junction on I-V characteristics of photovoltaic power converter

Tunnel junction is the crucial part for photovoltaic power converters, especially for those with the multi-junction structure. In this research, through changing growing temperature and the ratio of V-III precursor, four single-junction photovoltaic power converters with tunnel junction of different doping concentrations are fabricated. The I-V characteristics of four samples are measured, and also their power conversion efficiency and fill factors are calculated. It was found that the I-V curves of the samples exhibited significant differences as the doping concentration increased. Within an appropriate range, the photovoltaic power converter with higher doping concentration exhibits higher power conversion efficiency. However, when the doping concentration is too high, a reverse barrier appears inside the tunnel junction, manifesting as a “stair” I-V curve. This barrier will result in a reduction in device efficiency. This work provides important guidance for designing the doping concentration of tunnel junctions and fabricating high-performance photovoltaic power converters

The energy of random graphs

AbstractIn 1970s, Gutman introduced the concept of the energy E(G) for a simple graph G, which is defined as the sum of the absolute values of the eigenvalues of G. This graph invariant has attracted much attention, and many lower and upper bounds have been established for some classes of graphs among which bipartite graphs are of particular interest. But there are only a few graphs attaining the equalities of those bounds. We however obtain an exact estimate of the energy for almost all graphs by Wigner’s semi-circle law, which generalizes a result of Nikiforov. We further investigate the energy of random multipartite graphs by considering a generalization of Wigner matrix, and obtain some estimates of the energy for random multipartite graphs

In Situ Structural Health Monitoring of Full-Scale Wind Turbine Blades in Operation Based on Stereo Digital Image Correlation

Structural health monitoring (SHM) and the operational condition assessment of blades are greatly important for the operation of wind turbines that are at a high risk of disease in service for more than 5 years. Since certain types of blade faults only occur during wind turbine operation, it is more significant to perform in situ SHM of rotating full-scale blades than existing SHM of small-scale blades or static testing of full-scale blades. Considering that these blades are usually not prefabricated with relevant sensors, this study performed SHM and condition assessment of full-scale blades in operation with stereo digital image correlation. A self-calibration method adapted to the outdoors with a large field of view was introduced based on the speckled patterns. To accurately obtain the in- and off-plane deformation, a new reference frame is constructed at the center of the rotation of the blades. The 3D displacements of the points of interest (POIs) on the blade of a 2 MW wind turbine were characterized. Furthermore, the frequency spectrum of the measured 3D displacements of the blades was compared with the blades with the faults. The results showed that the introduced technique is a convenient and nondestructive technique that enables SHM of full-scale wind turbine blades in operation