Numerical study of the ternary Cahn–Hilliard fluids by using an efficient modified scalar auxiliary variable approach

2021 ◽  
pp. 105923
Author(s):  
Junxiang Yang ◽  
Junseok Kim
Keyword(s):  
Numerical Study ◽  
Auxiliary Variable ◽  
Variable Approach

Stochastic Multidisciplinary Analysis Under Epistemic Uncertainty

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Chen Liang ◽  
Sankaran Mahadevan ◽  
Shankar Sankararaman
Keyword(s):  
Model Uncertainty ◽  
Integral Transform ◽  
Epistemic Uncertainty ◽  
Interval Data ◽  
Auxiliary Variable ◽  
Data Uncertainty ◽  
System Level ◽  
Model Errors ◽  
Variable Approach ◽  
Multidisciplinary Analysis

This paper presents a probabilistic framework to include the effects of both aleatory and epistemic uncertainty sources in coupled multidisciplinary analysis (MDA). A likelihood-based decoupling approach has been previously developed for probabilistic analysis of multidisciplinary systems, but only with aleatory uncertainty in the inputs. This paper extends this approach to incorporate the effects of epistemic uncertainty arising from data uncertainty and model errors. Data uncertainty regarding input variables (due to sparse and interval data) is included through parametric or nonparametric distributions using the principle of likelihood. Model error is included in MDA through an auxiliary variable approach based on the probability integral transform. In the presence of natural variability, data uncertainty, and model uncertainty, the proposed methodology is employed to estimate the probability density functions (PDFs) of coupling variables as well as the subsystem and system level outputs that satisfy interdisciplinary compatibility. Global sensitivity analysis (GSA), which has previously considered only aleatory inputs and feedforward or monolithic problems, is extended in this paper to quantify the contribution of model uncertainty in feedback-coupled MDA by exploiting the auxiliary variable approach. The proposed methodology is demonstrated using a mathematical MDA problem and an electronic packaging application example featuring coupled thermal and electrical subsystem analyses. The results indicate that the proposed methodology can effectively quantify the uncertainty in MDA while maintaining computational efficiency.

scholarly journals Joint influence of measurement errors and randomized response technique on mean estimation under stratified double sampling

2021 ◽  
Vol 5 (1) ◽  
pp. 192-199
Author(s):  
Ronald Onyango ◽  
◽  
Brian Oduor ◽  
Francis Odundo ◽  
◽  
...  
Keyword(s):  
Measurement Errors ◽  
Mean Squared Error ◽  
Numerical Study ◽  
Real Data ◽  
Auxiliary Variable ◽  
Randomized Response Technique ◽  
Randomized Response ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Joint Influence

The present study proposes a generalized mean estimator for a sensitive variable using a non-sensitive auxiliary variable in the presence of measurement errors based on the Randomized Response Technique (RRT). Expressions for the bias and mean squared error for the proposed estimator are correctly derived up to the first order of approximation. Furthermore, the optimum conditions and minimum mean squared error for the proposed estimator are determined. The efficiency of the proposed estimator is studied both theoretically and numerically using simulated and real data sets. The numerical study reveals that the use of the Randomized Response Technique (RRT) in a survey contaminated with measurement errors increases the variances and mean squared errors of estimators of the finite population mean.

scholarly journals Ratio Type Estimation Using the Knowledge of the Auxiliary Variable for Ranking and Estimating

2017 ◽  
Vol 6 (2) ◽  
pp. 21 ◽  
Author(s):  
Carlos N. Bouza ◽  
Amer Ibrahim Al-Omari ◽  
Agustín Santiago ◽  
Jose M. Sautto
Keyword(s):  
Solid Waste ◽  
Random Sampling ◽  
Numerical Study ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Ranked Set Sampling ◽  
Using Data

In this paper, the behavior of ranked set sampling is analyzed considering the knowledge of the auxiliary variable. The suggested estimators are compared with their simple random sampling counterparts. A numerical study is developed using data from a study developed on the contamination due to burning compost from solid waste from hospitals.

scholarly journals Almost Unbiased Ratio cum Product Estimator for Finite Population Mean with Known Median in Simple Random Sampling

2017 ◽  
Vol 1 ◽  
pp. 1-14
Author(s):  
Subramani Jambulingam ◽  
Ajith S. Master
Keyword(s):  
Random Sampling ◽  
Mean Squared Error ◽  
Numerical Study ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Study Variable ◽  
Population Mean ◽  
Squared Error ◽  
Product Estimator ◽  
Almost Unbiased

Introduction: In sampling theory, different procedures are used to obtain the efficient estimator of the population mean. The commonly used method is to obtain the estimator of the population mean is simple random sampling without replacement when there is no auxiliary variable is available. There are methods that use auxiliary information of the study characteristics. If the auxiliary variable is correlated with study variable, number of estimators are widely available in the literature.Objective: This study deals with a new ratio cum product estimator is developed for the estimation of population mean of the study variable with the known median of the auxiliary variable in simple random sampling.Materials and Methods: The bias and mean squared error of proposed estimator are derived and compared with that of the existing estimators by analytically and numerically.Results: The proposed estimator is less biased and mean squared error is less than that of the existing estimators and from the numerical study, under some known natural populations, the bias of proposed estimator is approximately zero and the mean squared error ranged from 6.83 to 66429.21 and percentage relative efficiencies ranged from 103.65 to 2858.75.Conclusion: The proposed estimator under optimum conditions is almost unbiased and performs better than all other existing estimators.Nepalese Journal of Statistics, 2017, Vol. 1, 1-14

Fast algorithm for nonlocal Allen–Cahn equation with scalar auxiliary variable approach

2021 ◽  
pp. 107805
Author(s):  
Changhui Yao ◽  
Huijun Fan ◽  
Yanmin Zhao ◽  
Yanhua Shi ◽  
Fenling Wang
Keyword(s):  
Fast Algorithm ◽  
Auxiliary Variable ◽  
Cahn Equation ◽  
Variable Approach
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