scholarly journals Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media

2001 ◽  
Vol 40 (8) ◽  
pp. 1554 ◽  
Author(s):  
M. A. Al-Habash
Keyword(s):  
Mathematical Model ◽  
Probability Density Function ◽  
Laser Beam ◽  
Probability Density ◽  
Density Function

A Skewed Two-Dimensional Probability Density Function for Methane-Air Turbulent Diffusion Flames

2010 ◽  
Author(s):  
Mohsen Abou-Ellail ◽  
Ryo S. Amano ◽  
Samer Elhaw ◽  
Karam Beshay ◽  
Hatem Kayed
Keyword(s):  
Mathematical Model ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Dissipation Rate ◽  
Diffusion Flames ◽  
Mixture Fraction ◽  
Two Dimensional ◽  
Flamelet Model ◽  
The Mean

The present paper describes a mathematical model for turbulent methane-air jet diffusion flames. The mathematical model solves density-weighted governing equations for momentum, mass continuity, turbulent kinetic energy and its dissipation rate. The combustion model solves density-weighted transport equations for the mixture fraction “f”, its variance “g” and its skewness “s”. These variables are used to compute one part of the probability density function (PDF) in mixture fraction domain. The second part of the PDF is computed from the numerical solutions of the mixture fraction dissipation rate “χ” and its variance χ˜″2. The resulting two-dimensional PDF is defined in the mixture-fraction-scalar-dissipation-rate 2D space. The flamelet combustion sub-model is used to compute the mean flame temperature, density and species mass fractions. The flamelet model provides instantaneous state relationships for the stretched flamelets up to the extinction limit. The mean flame properties are computed through the integration of the stretched flamelet state relationships over the two-dimensional PDF. The present 2D probability density function model can predict rim-attached flames as well as unstable lifted flames. This is because the flamelet model provides information on the flame instability arising from the stretching effects of highspeed flowing gases. The new two-dimensional probability density function is used to predict the flame properties of a free jet methane-air flame for which experimental data exists.

scholarly journals Computational Methods in Problems of Subjective Assessment of Investment Decisions Effectiveness

2020 ◽  
pp. 77-82
Author(s):  
E.V. Danko ◽  
Ye.K. Yergaliyev ◽  
M.N. Madiyarov
Keyword(s):  
Mathematical Model ◽  
Probability Density Function ◽  
Utility Function ◽  
Probability Density ◽  
Density Function ◽  
Real Life ◽  
Investment Project ◽  
Random Variable ◽  
Main Element ◽  
Subjective Utility

The paper describes the implementation of investment projects under conditions of uncertainty. In the developed mathematical model, the effectiveness of an investment project is evaluated by the NPV index. This index is considered a random variable that can be estimated by an investor to within a segment [NPV1;NPV2]. The main difficulties of the decision-making process arise when the segment [NPV1;NPV2] includes zero value. In the developed model, we use the probability density function of NPV value in the form of Pearson curves of the first type. This paper discusses in detail some particular moments, which are to be taken into consideration while choosing a specific type of probability density function of NPV. The main element of the proposed model is the subjective utility function. Many questions regarding the usage of this function in practice are also extensively reviewed in this article. The main requirement for successful usage of the subjective utility function in real life is a well-calculated chapter of scenario analysis of an investment project. This chapter is present in almost all modern business plans. The practical application of the developed mathematical model improves the quality of decisions concerning the investment of funds into projects.

scholarly journals Probability density function of the intensity of a laser beam propagating in the maritime environment

2011 ◽  
Vol 19 (21) ◽  
pp. 20322 ◽  
Author(s):  
Olga Korotkova ◽  
Svetlana Avramov-Zamurovic ◽  
Reza Malek-Madani ◽  
Charles Nelson
Keyword(s):  
Probability Density Function ◽  
Laser Beam ◽  
Probability Density ◽  
Density Function ◽  
Maritime Environment
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