An Inverse Solution Methodology for Estimating Diffusivity Coefficient of Gases in Bitumen from Pressure-Decay Data

2006 ◽  
Author(s):  
Hussain Sheikha ◽  
Anil Mehrotra ◽  
Mehran Pooladi-Darvish
Keyword(s):  
Inverse Solution ◽  
Diffusivity Coefficient ◽  
Decay Data ◽  
Pressure Decay ◽  
Solution Methodology

Development of Graphical Methods for Estimating the Diffusivity Coefficient of Gases in Bitumen from Pressure-Decay Data

2005 ◽  
Vol 19 (5) ◽  
pp. 2041-2049 ◽  
Author(s):  
Hussain Sheikha ◽  
Mehran Pooladi-Darvish ◽  
Anil K. Mehrotra
Keyword(s):  
Graphical Methods ◽  
Diffusivity Coefficient ◽  
Decay Data ◽  
Pressure Decay

scholarly journals Regression Analysis of the Left-ventricular Isochoric Pressure Decay of the Heart: Four or Five Model Parameters?

2015 ◽  
Vol 4 ◽  
pp. 53
Author(s):  
John Langer
Keyword(s):  
Guinea Pig ◽  
Kinematic Model ◽  
Parametric Model ◽  
Left Ventricular ◽  
Model Parameters ◽  
Decay Data ◽  
Pressure Decay ◽  
Rat Hearts ◽  
Regression Error ◽  
Damped Oscillation

BACKGROUND: Isochoric (isovolumic) cardiac pressure decay data were previously described by a four-parametric logistic (tangens hyperbolicus) regression model (Langer model). However, a five-parametric kinematic model (Chung model), according to the differential equation of damped oscillation, was recently introduced to describe the isochoric pressure fall. The present study clarifies (a/) whether these five parameters can be reliably estimated from empirical pressure decay data and if the model excels the four-parametric one, and (b/) whether the kinematic Chung model validly describes these pressure decays. METHODS: High-fidelity intraventricular pressure decay data from 1203 isolated working guinea pig and rat hearts were analyzed by both models. RESULTS: Most cases present with a higher regression error in the five-parametric kinematic model, the median ratio (F value) of its regression variance by those of the four-parametric logistic model is 1.004 (95 per cent confidence interval: 1.002 to 1.006) in in the guinea pig as well as in the rat group. Additionally, the parameters of both models were estimated from the first and second half of the decay phase separately to check for the models' validity.  The five-parametric model yields significantly non-constant parameters more often than the four-parametric model. CONCLUSION: (a) the five parameters of the kinematic Chung model remain underdetermined by the empirical pressure data, and {b) this five-parametric model does not provide a valid description of the isochoric cardiac pressure decay.

Empirical model approach for the evaluation of pH and conductivity on pollutant diffusion in soil environment

2019 ◽  
Author(s):  
Chem Int
Keyword(s):  
Mathematical Model ◽  
Quadratic Equation ◽  
Diffusivity Coefficient ◽  
Soil Environment ◽  
Irreversible Reaction ◽  
Chemical Pollutant ◽  
The Mathematical Model ◽  
Coefficient Of Diffusion ◽  
Level Of Agreement ◽  
Model Approach

This work is aimed at developing a mathematical model equation that can be used to predict the fate of contaminant in the soil environment. The mathematical model was developed based on the fundamental laws of conservation and the equation of continuity given asand was resolved to obtain a quadratic equation of the form C(X) = DX2+vX+f. The developed equation was then used to fit the experimental data that were obtained from the Physio-chemical analysis of the soil samples which were obtained at various depths; within the vicinity of the H & H Asphalt plant Company, located at Enito 3 in Ahoada West L.G.A, River State, Nigeria. The Experimental and Model results obtained from the Calculation and Simulation of the developed models were compared numerically and graphically as presented in this work. It was observed that there is reasonable level of agreement between the three results. The polynomial of the curve was established to ascertain the validity of the model; this was done for all the parameters that were analyzed. From the findings the model developed can be used to predict the concentration of a chemical pollutant at various depths. The reliability of the model developed was established giving the fact that through this quadratic equation the diffusivity (coefficient of diffusion), the water velocity and the irreversible reaction decay rate could be determined.

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