Hemispherical Solar Distiller With Truncated Circular Cone-Shaped Reflector Mirrors ( TCC-RM)

The present study aims to achieve the highest cumulative yield of the hemispherical distillers, by designing and constructing new reflector mirrors, which are truncated circular cone-shaped reflector mirrors (TCC-RM). To obtain the optimum inclination of TCC-RM that achieves a highest hemispherical distiller’s performance, eight inclination angles (10o, 15o, 20o, 25o, 30o, 35o, 40o and 45o with vertical) was experimentally studied. To achieve this, a series of experimental tests were carried out on the three hemispherical solar distillers, the first represents the reference distiller (traditional hemispherical solar distiller- THSD) and the other two devices are the hemispherical solar distiller with truncated circular cone-shaped reflector mirrors (HSD-TCCRM) with different inclination angles. The experimental results indicate that utilizing TCC-RM with a 25o inclination angle achieve the maximum cumulative yield of 8.35 L/m2 with an improvement of 42.74% compared to THSD. While the utilization of TCC-RM with the inclination angles by 30o, 35o, 20o, 40o, and 15o achieves the cumulative yield of 7.9, 7.3, 7.05, 6.67, 6.6 L/m2 compared with 5.85 L/m2 for THSD. On the contrary, adjusting the inclination angle of TCC-RM at 10o, and 45o affects negatively the cumulative yield of the HSD with TCC-RM in comparison with THSD. Based on the data of cumulative yield, daily efficiency, and the economics analysis its recommended to utilized TCC-RM with a 25o inclination angle to achieve the highest performance and minimum distillate cost of hemispherical solar distillers.

Lower bound of extremal Pompeiu radius for half of cone

Lower estimates are established for the smallest radius of a ball, in which a given set is the Pompeiu set. As the set, the half of the straight circular cone with radius of base 1 and attitude $h > 1$ is considered. For $h > 3$ the exact value of extreme Pompeiu radius is obtained.

Tiling Efflorescence of Expanding Kernels in a Fixed Periodic Array

Continually expanding periodically translated kernels on the two dimensional grid can yield interesting, beau- tiful and even familiar patterns. For example, expand- ing circular pillbox shaped kernels on a hexagonal grid, adding when there is overlap, yields patterns includ- ing maximally packed circles and a triquetra-type three petal structure used to represent the trinity in Chris- tianity. Continued expansion yields the flower-of-life used extensively in art and architecture. Additional expansion yields an even more interesting emerging ef- florescence of periodic functions. Example images are given for the case of circular pillbox and circular cone shaped kernels. Using Fourier analysis, fundamental properties of these patterns are analyzed. As a func- tion of expansion, some effloresced functions asymp- totically approach fixed points or limit cycles. Most interesting is the case where the efflorescence never repeats. Video links are provided for viewing efflores- cence in real time.

A Computationally Efficient Reconstruction Algorithm for Circular Cone-Beam Computed Tomography Using Shallow Neural Networks

Circular cone-beam (CCB) Computed Tomography (CT) has become an integral part of industrial quality control, materials science and medical imaging. The need to acquire and process each scan in a short time naturally leads to trade-offs between speed and reconstruction quality, creating a need for fast reconstruction algorithms capable of creating accurate reconstructions from limited data. In this paper, we introduce the Neural Network Feldkamp–Davis–Kress (NN-FDK) algorithm. This algorithm adds a machine learning component to the FDK algorithm to improve its reconstruction accuracy while maintaining its computational efficiency. Moreover, the NN-FDK algorithm is designed such that it has low training data requirements and is fast to train. This ensures that the proposed algorithm can be used to improve image quality in high-throughput CT scanning settings, where FDK is currently used to keep pace with the acquisition speed using readily available computational resources. We compare the NN-FDK algorithm to two standard CT reconstruction algorithms and to two popular deep neural networks trained to remove reconstruction artifacts from the 2D slices of an FDK reconstruction. We show that the NN-FDK reconstruction algorithm is substantially faster in computing a reconstruction than all the tested alternative methods except for the standard FDK algorithm and we show it can compute accurate CCB CT reconstructions in cases of high noise, a low number of projection angles or large cone angles. Moreover, we show that the training time of an NN-FDK network is orders of magnitude lower than the considered deep neural networks, with only a slight reduction in reconstruction accuracy.