Single-peak distribution model of particulate size for welding aerosols

A large number of particulate size distributions of welding aerosols are measured by means of DMPS method, several distribution types are presented. Among them the single peak distribution is the basic composing unit of particulate size. The research on the mathematic models and distributions functions shows that the single peak distribution features the log normal distribution. The diagram estimating method (DEM) is a concise approach to dealing with distribution types, obtaining distribution functions for the particulate sizes of welding aerosols. It proves that the distribution function of particulate size possesses the extending property, being from quantity distribution to volume, as well as high order moment distributions, with K S method verifying the application of single peak distribution and of DEM.

Mathematical Insight into Moderate Inversion Gate Delay Variability for Ultradeep Submicron Digital Circuit Design

Voltage scaling has been extensively used in industry for decades to reduce power consumption.In recent years,exploring digital circuit operation in moderate inversion has created an interest among researchers due to its immense capability to provide a perfect tradeoff between high performance and low energy operation.But circuits operating in moderate inversion are susceptible to process variations and variability.To compute variability,statistical parameters such as the probability density function(PDF)and cumulative distribution function(CDF)are required.This paper presents an analytical model framework for delay calculations utilizing log skew normal distribution for ultradeep submicron technology nodes up to 22 nm.The CDF of the proposed model is utilized to calculate minimum and maximum delays with 3σ-accuracy providing better accuracy than the conventional methods.The obtained results are also compared with Monte Carlo simulations with errors lying within the acceptable range of 2%-4%.

Spatio-temporal Rainfall Distribution and Markov Chain Analogue Year Stochastic Daily Rainfall Model in Ethiopia

This paper aims at the spatiotemporal distribution of rainfall in Ethiopia and developing stochastic daily rainfall model.Particularly,in this study,we used a Markov Chain Analogue Year(MCAY)model that is,Markov Chain with Analogue year(AY)component is used to model the occurrence process of daily rainfall and the intensity or amount of rainfall on wet days is described using Weibull,Log normal,mixed exponential and Gamma distributions.The MCAY model best describes the occurrence process of daily rainfall,this is due to the AY component included in the MC to model the frequency of daily rainfall.Then,by combining the occurrence process model and amount process model,we developed Markov Chain Analogue Year Weibull model(MCAYWBM),Markov Chain Analogue Year Log normal model(MCAYLNM),Markov Chain Analogue Year mixed exponential model(MCAYMEM)and Markov Chain Analogue Year gamma model(MCAYGM).The performance of the models is assessed by taking daily rainfall data from 21 weather stations(ranging from 1 January 1984–31 December 2018).The data is obtained from Ethiopia National Meteorology Agency(ENMA).The result shows that MCAYWBM,MCAYMEM and MCAYGM performs very well in the simulation of daily rainfall process in Ethiopia and their performances are nearly the same with a slight difference between them compared to MCAYLNM.The mean absolute percentage error(MAPE)in the four models:MCAYGM,MCAYWBM,MAYMEM and MCAYLNM are 2.16%,2.27%,2.25%and 11.41%respectively.Hence,MCAYGM,MCAYWBM,MAYMEM models have shown an excellent performance compared to MCAYLNM.In general,the light tailed distributions:Weibull,gamma and mixed exponential distributions are appropriate probability distributions to model the intensity of daily rainfall in Ethiopia especially,when these distributions are combined with MCAYM.