A model for orientation effects in electron‐transfer reactions

A method for solving the single‐particle Schrödinger equation with an oblate spheroidal potential of finite depth is presented. The wave functions are then used to calculate the matrix element T_BA which appears in theories of nonadiabatic electron transfer. The results illustrate the effects of mutual orientation and separation of the two centers on TBA. Trends in these results are discussed in terms of geometrical and nodal structure effects. Analytical expressions related to T_BA for states of spherical wells are presented and used to analyze the nodal structure effects for T_BA for the spheroidal wells

Tensile and fatigue properties of Inconel 718 at cryogenic temperatures

Tests to determine the tensile and fatigue properties of Inconel 718 at cryogenic temperatures show that the alloy increases in strength at low temperatures, with very little change in toughness. The effect of surface finish and grain size on the fatigue properties was also determined

Heat transfer and evaporation in spray cooling of hot gas flows, including the effect of nozzle design

This study investigates the influence of spray nozzle internal geometry on heat transfer performance and the resultant power requirements. An experimental apparatus was designed and built, which allowed for close control of the heat transfer from air to water and the required energy for droplet production. The apparatus allowed for simultaneous measurements of heat transfer rate from the gas to the spray droplets and the pumping power requirements for the sprayed liquid. A spray chamber was constructed in the form of a Perspex cylinder, 372 mm internal diameter and 372 mm height, mounted on its vertical axis. Thermocouples, humidity sensors, and pressure sensors were used to measure the temperature difference of the air and water, the humidity difference of the air, and the pressure drop across the nozzle. The spray nozzles have been installed at the centre of the upper cover plate directed along the cylinder axis. The heat and mass transfer process was carried out in a counter current flow. Two different nozzle designs were the subject of this investigation. The pressure swirl nozzle works on liquid pressure alone. Droplet formation and size is influenced by changes of the internal geometry and liquid pressure. An effervescent two fluid atomiser with internal mixing was tested. The influence of changes in gas bubble and exit orifice geometry on droplet size and formation was investigated. Analysis of the heat transfer process is based on the energy balance for the whole cylinder. This analysis allows for the determination of the nozzle with the best performance characteristics. From the required energy to produce the droplets and the rate of heat transfer, a new equation for the index of energy performance, was defined. A Laser Doppler Analyser was used to determine the droplet size and velocity for the low pressure nozzles and this data was compared with the existing theory. The droplet distribution of the spray nozzles was determined for various configuration. The measured droplet size was below the calculated droplet size using the derived equations from the literature. Photographs of the spray angle at different liquid pressures were taken for digital analysis. The spray angle showed reasonable agreement with the literature. A three dimensional numerical model was designed to simulate the heat transfer process inside the spray chamber using PHOENICS, a Computational Fluid Dynamics (CFD) software. The software modelled the heat and mass transfer inside the spray chamber. This model then allowed for the testing of different droplet distributions, formations, and their influence on the heat transfer process. In order to validate the results, the necessary variables such as the gas mass flow, liquid mass flow rate, droplet size, spray angle and scatter, hot air inlet temperature, were obtained from the experimental data. The result of the simulation is the air outlet temperature and humidity of the spray chamber. The internal 3D flow field is solved with the Lagrangian and Eulerian equation including the disturbance, solved with the k-epsilon turbulence model, created by the spray droplets. Four different pressure swirl configurations were simulated. Every configuration had five different pressure points. Every pressure point was simulated individually in order to find out if the numerical simulation software was able to predict the correct result for different liquid mass flow rates without altering the boundary setting and parameters. The heat transfer process was found to depend on the droplet size and distribution produced by the spray nozzle. A comparison of the experimental data with the simulation results demonstrated the accuracy of the CFD model. The temperature accuracy was ±5.9% and for the humidity ±12% on average for all simulations. It was found that the heat transfer of the effervescent atomiser depends on the mass ALR and that the highest heat transfer was measured when it was operating with an ALR of 0.1. The tested effervescent atomiser was found to be strongly influenced by the atomising air, an effectiveness of 93% achieved. The change of the internal geometries had no significant influence on the heat transfer rates. The change of the internal geometry, especially the exit orifice diameter, had a strong influence on the pressure swirl nozzle performance, which started at 85% and reached a maximum of 95%. It was found that the pressure requirement for the 4.7 mm exit orifice was only 20% of the pressure requirement of the 2.5 mm exit orifice in order to achieve the same cooling performance. The pressure swirl needed for all flow rates approximately 20 times less energy to achieve the same cooling as the effervescent nozzle

On the Cost of Essentially Fair Clusterings

Clustering is a fundamental tool in data mining. It partitions points into groups (clusters) and may be used to make decisions for each point based on its group. However, this process may harm protected (minority) classes if the clustering algorithm does not adequately represent them in desirable clusters -- especially if the data is already biased. At NIPS 2017, Chierichetti et al. proposed a model for fair clustering requiring the representation in each cluster to (approximately) preserve the global fraction of each protected class. Restricting to two protected classes, they developed both a 4-approximation for the fair $k$-center problem and a $O(t)$-approximation for the fair $k$-median problem, where $t$ is a parameter for the fairness model. For multiple protected classes, the best known result is a 14-approximation for fair $k$-center. We extend and improve the known results. Firstly, we give a 5-approximation for the fair $k$-center problem with multiple protected classes. Secondly, we propose a relaxed fairness notion under which we can give bicriteria constant-factor approximations for all of the classical clustering objectives $k$-center, $k$-supplier, $k$-median, $k$-means and facility location. The latter approximations are achieved by a framework that takes an arbitrary existing unfair (integral) solution and a fair (fractional) LP solution and combines them into an essentially fair clustering with a weakly supervised rounding scheme. In this way, a fair clustering can be established belatedly, in a situation where the centers are already fixed

The California-Mexico agriculture connection

International trade ; Agriculture - California ; California ; Mexico ; Agriculture - Mexico